Help I don’t understand at all
Answer:
[tex]1)\ \ 4h^2-13h+6\\2)\ \ 7x^3y^2-x^2y+1\\3)\ \ -7n+2\\4)\ \ -8m+4[/tex]
Step-by-step explanation:
1.
Simplify the expression by combining like terms. Remember, like terms have the same variable part, to simplify these terms, one performs operations between the coefficients. Please note that a variable with an exponent is not the same as a variable without the exponent. A term with no variable part is referred to as a constant, constants are like terms.
[tex]2h^2-7h+2h^2-h+6+4h-9h[/tex]
[tex](2h^2+2h^2)+(-7h-h+4h-9h)+(6)[/tex]
[tex]4h^2-13h+6[/tex]
2.
Use a very similar method to solve this problem as used in the first. Please note that all of the rules mentioned in the first problem also apply to this problem; for that matter, the rules mentioned in the first problem generally apply to any pre-algebra problem.
[tex]8x^3y^2-7x^2y+8x-4-x^3y^2+2x^2y+4x^2y-8x+5[/tex]
[tex](8x^3y^2-x^3y^2)+(-7x^2y+2x^2y+4x^2y)+(8x-8x)+(-4+5)[/tex]
[tex]7x^3y^2-x^2y+1[/tex]
3.
Use the same rules as applied in the first problem. Also, keep the distributive property in mind. In simple terms, the distributive property states the following ([tex]a(b+c)=(a)(b)+(a)(c)=ab+ac[/tex]). Also note, a term raised to an exponent is equal to the term times itself the number of times the exponent indicates. In the event that the term raised to an exponent is a constant, one can simplify it. Apply these properties here,
[tex]-2(8n+1)-(5-9n)+3^2[/tex]
[tex]-2(8n+1)-(5-9n)+(3*3)[/tex]
[tex]-2(8n+1)-(5-9n)+9[/tex]
[tex](-2)(8n)+(-2)(1)+(-)(5)+(-)(-9n)+9[/tex]
[tex]-16n-2-5+9n+9[/tex]
[tex](-16n+9n)+(-2-5+9)[/tex]
[tex]-7n+2[/tex]
4.
The same method used to solve problem (3) can be applied to this problem.
[tex]\frac{1}{2}(10-8m+6m^2)-(3m^2+4m-7)-2^3[/tex]
[tex]\frac{1}{2}(10-8m+6m^2)-(3m^2+4m-7)-(2)(2)(2)[/tex]
[tex](\frac{1}{2})(10)+(\frac{1}{2})(-8m)+(\frac{1}{2})(6m^2})+(-)(3m^2)+(-1)(4m)+(-1)(-7)-8[/tex]
[tex]5-4m+3m^2-3m^2-4m+7-8[/tex]
[tex](-3m^2-3m^2)+(-4m-4m)+(5+7-8)[/tex]
[tex]-8m+4[/tex]
Twice a number increased by the product of the number and fourteen results in forty eight
Answer:
Let x = the number. Then you have:
2x + 14x = 48 Collect like terms
16x = 48 Divide both sides by 16
x = 3
PLEASE MARK AS BRAINLIEST ANSWER
The number that satisfies the given statement is 3.
We are given that twice a number increased by the product of the number and 14 results in 48.
We will find the value of the number that we used in the given above statement.
Understand the meaning of the keywords used in the statement.Increased means addition.
Product means multiplication.
Results mean equal to sign.
Let's write the given statement in equation form.
Consider P = the number
Twice a number = 2P
Increased = +
Products of the number and 14 = P x 14
Results in 48 = equals 48.
Combining all the above we get,
2P + P x 14 = 48
2P + 14P = 48
16P = 48
P = 48 / 16
P = 3
Thus the number that satisfies the given statement is 3.
Learn more about similar problems here:
https://brainly.com/question/17618748
#SPJ2
Clara travels from her home to Stoke.
The distance from her home to Stoke is 100 miles.
She travels at an average speed of 50 miles per hour.
She stops for 20 minutes on the journey. Clara arrives in Stoke at 10:10 am.
At what time did she leave home?
Answer:
7:50 am
Step-by-step explanation:
Clara took 2 hours to reach, and she took a 20 min break, so she left at 7:50 and arrived at 10:10.
Answer:
7:50
Step-by-step explanation:
50 miles per hour/50 miles per 60 min.
50 miles + 50 miles = 100 miles.
if 50 miles takes 1 hour, 100 miles would equal to 2 hours.
considering clara took a 20 min break, thats 2 hours and 20 minutes.. subtract that from the time she arrived and you would get 7:50
Which shows the correct substitution of the values a, b, and c from the equation -2 = -x + x2 – 4 into the quadratic
formula?
Quadratic formula: x =
-bb2-4ac
2 a
Ox=
-(-1){V - 1)2 - 4(1)(-4)
2(1)
O x=-11/12-46- 1)( - 4)
2(-1)
O x= -13V (1)? - 4( - 1)(-2)
2(-1)
O x=-(-1)+7(-1)2 - 4(1)(-2)
2(1)
The values of a, b, c are obtained from the given equation, by equation
in the form in which it is equal to 0.
The correct substitution of the values a, b, and c from the equation -2 = -x + x² - 4 is the option;
[tex]\underline{x = \dfrac{-1 \pm \sqrt{1^2 - 4 \cdot (-1) \cdot (-2)} }{2 \cdot (-1)}}[/tex]Which is the method by which the values of a, b, and c are substituted?Given:
The quadratic formula is presented as follows;
[tex]x = \mathbf{ \dfrac{-b \pm \sqrt{b^2 - 4 \cdot a \cdot c} }{2 \cdot a}}[/tex]
The given equation is presented as follows;
-2 = -x + x² - 4
Which gives;
0 = -x + x² - 4 + 2 = -x + x² - 2
-x + x² - 2 = 0
Therefore, we have;
[tex]x = \mathbf{ \dfrac{-1 \pm \sqrt{1^2 - 4 \times (-1) \times (-2)} }{2 \times (-1)}}[/tex]The correct option is therefore;
[tex]x = \dfrac{-1 \pm \sqrt{1^2 - 4 \cdot (-1) \cdot (-2)} }{2 \cdot (-1)}[/tex]Learn more about the quadratic formula here:
https://brainly.com/question/1630251
Please help me answer this question?
Answer:
[tex]P'(x)=2.2-0.12x[/tex]
Step-by-step explanation:
start by finding [tex]P(x) = R(x)-C(x)[/tex]
[tex]P(x)=3x-0.06x^2-286-0.8x[/tex]
to find P'(x), you take the derivative of P(x)
[tex]P'(x)=\frac{d}{dx} (2.2x-286-0.06x^2)[/tex]
[tex]\frac{d}{dx} (2.2x-286-0.06x^2)=2.2-0.12x[/tex]
so [tex]P'(x)=2.2-0.12x[/tex]
Câu 99: Cho hàm số f x xác định trên ℝ , bảng biến thiên của hàm số f x như sau.
x 1 1 3
f x | 0 |
f x
0 0
4
Mệnh đề nào dưới đây đúng?
A. Hàm số f x đồng biến trên 1;.
B. Hàm số f x đồng biến trên ; 1 và 3;.
C. Hàm số f x nghịch biến trên ; 1.
D. Hàm số f x đồng biến trên ; 1 3; .
Answer:
i doesn,t understand this language
It is known that 10% of adults can pass a fitness test. What is the probability at most 12 adults in a
sample of 100 adults pass this fitness test?
Using the normal distribution, there is a 0.7967 = 79.67% probability that at most 12 adults in a sample of 100 adults pass this fitness test.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters of the binomial distribution are given by:
p = 0.1, n = 100.
Hence the mean and the standard deviation for the approximation are given by:
[tex]\mu = np = 100 \times 0.1 = 10[/tex][tex]\sigma = \sqrt{np(1-p)} = \sqrt{100 \times 0.1 \times 0.9} = 3[/tex]The probability at most 12 adults in a sample of 100 adults pass this fitness test, using continuity correction, is P(X < 12.5), which is the p-value of Z when X = 12.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12.5 - 10}{3}[/tex]
Z = 0.83
Z = 0.83 has a p-value of 0.7967.
0.7967 = 79.67% probability that at most 12 adults in a sample of 100 adults pass this fitness test.
More can be learned about the normal distribution at https://brainly.com/question/28159597
#SPJ1
helppppp
Find the value of x.
A. 176
B. 128
C. 256
D. 74
Answer: Choice B) 128
Explanation:
We'll add up the given arc measures and then cut the result in half to get the angle formed by the intersecting chords (that subtend the arcs in question).
chord angle = (arc1+arc2)/2
x = (54+202)/2
x = 256/2
x = 128
Answer:
128
Step-by-step explanation:
Angle Formed by Two Chords = 1/2(SUM of Intercepted Arcs)
x = 1/2 (54+202)
x = 1/2 (256)
x =128
Lesson 9.6: Steady-State Analysis.) Consider a particular data set of 100,000 stationary waiting times obtained from a large queueing system. Suppose your goal is to get a confidence interval for the unknown mean. Would you rather use (a) 50 batches of 2000 observations or (b) 10000 batches of 10 observations each?
Answer:
I would rather use:
(b) 10,000 batches of 10 observations each.
Step-by-step explanation:
It is easier to have 10,000 batches of 10 observations each than to have 50 batches of 2,000 observations. Human errors are reduced with fewer observations. For example, Hadoop, a framework used for storing and processing big data, relies on batch processing. Using batch processing that divides the 100,000 stationary waiting times into 10 observations with 10,000 batches each is more efficient than having 2,000 observations with 50 batches each.
A test is worth 30 points. Multiple-choice questions are worth 2 point and short-answer questions are worth 3 points. If the test has 13 questions, how many multiple-choice questions are there?
If x , 2x and 50° are the interior angle of the triangle, find the unknown angle.
Answer:
40°
Step-by-step explanation:
x +2x+50=180 [sum of interior angles of a triangle]
or,3x=180-50
or,x=130/3
x=130/3
2x=2×130/3
what is a cell and why it is necessary
Cells are the basic building blocks of living things. The human body is composed of trillions of cells, all with their own specialised function. Cells are the basic structures of all living organisms.
IMPORTANCECells provide structure for the body, take in nutrients from food and carry out important functions.
I HOPE THIS WILL HELP YOU IF NOT THEN SORRYHAVE A GREAT DAY :)
6x=1/2(2X +7)
Solve for x
Answer:
Step-by-step explanation:
6x=1/2(2x +7) Multiply both sides by 2
2*6x = 1/2(2x + 7)*2
12x = 2x + 7 Subtract 2x from sides
12x-2x =2x-2x+7
10x = 7 Divide by 10
x = 7/10
x = 0.7
Let's check it
6(0.7) = 4.2
1/2 (2*0.7 + 7)
1/2 (1.4 + 7)
1/2 ( 8.4)
4.2
Both sides check. The answer must be x = 0.7
Find the area of the shaded regions:
QUICKLY!!!!!
Answer:
[tex]41.89\ cm^2[/tex]
Step-by-step explanation:
[tex]We\ are\ given:\\In\ two\ concentric\ circles,\\OD=3\ cm\\BC=4\ cm\\\angle DOB=\angle AOC=120\\Now,\\We\ know\ that:\\Area\ of\ a\ sector\ with\ a\ central\ angle\ \theta\ and\ a\ radius\ r\ is:\\A=\frac{\theta}{360}* \pi r^2\\Here,\\Area\ between\ the\ sectors=Area\ of\ Larger\ Sector - Area\ of\ smaller\ sector=\frac{\theta}{360}*\pi(R^2-r^2),\ where\ R\ and\ r\ are\ radii\ of\ the\ respective\ circles\ and\\ \theta\ is\ the\ common\ central\ angle.\\Here,\\R=4+3=7\ cm\\r=3\ cm\\ \theta=120\\ Hence,[/tex]
[tex]Area\ of\ the\ shaded\ region=\frac{120}{360}*\pi(7^2-3^2)=\frac{1}{3}*\pi(49-9)=\frac{1}{3}*\pi(40) \approx 41.89\ cm^2[/tex]
Please help me to find out the answer
Answer:
8.204786801 in
Step-by-step explanation:
cos (79°) = BE/BG= adjacent/hypotenuse
cos ( 79°) = BE/43 in
BE = cos (79°) × 43 in= 8.204786801 in
Find a pair of polar coordinates for the point with rectangular coordinates (5, –5).
Answer:
(5*sqrt(2), 5pi/4)
Step-by-step explanation:
In Polar coordinates, tan(theta)=y/x and r=sqrt(x^2+y^2)
tan(theta)=-5/5=-1. Theta=5pi/4
r=sqrt(5^2+5^2)=5*sqrt(2)
Hence the Polar coordinate is (5*sqrt(2), 5pi/4)
The polar coordinate is [tex](5\sqrt{2},\frac{-\pi }{4} )[/tex].
What is polar coordinate system?The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
How to convert rectangular coordinates to polar coordinates?To convert rectangular coordinate (x, y) to polar coordinate(r, θ) by using some formula
tanθ = y/x and [tex]r =\sqrt{x^{2} +y^{2} }[/tex]
According to the given question
We have
A rectangular coordinate (5, -5).
⇒ x = 5 and y = -5
Therefore,
[tex]r=\sqrt{(5)^{2} +(-5)^{2} } =\sqrt{25+25} =\sqrt{50} =5\sqrt{2}[/tex]
and
tanθ = [tex]\frac{-5}{5} =-1[/tex]
⇒ θ = [tex]tan^{-1} (-1)[/tex] = [tex]-\frac{\pi }{4}[/tex]
Therefore, the polar coordinate is [tex](5\sqrt{2},\frac{-\pi }{4} )[/tex].
Learn more about polar coordinates here:
https://brainly.com/question/1269731
#SPJ2
Complete the equation describing how
x and y are related.
X
0
1
2
3
5
6
у
5
6
7
8
9
10
y = x + [?]
Enter the answer that belongs in ?).
Answer:
y= x + 5
Step-by-step explanation:
it is clearly shown
somone please help asap! i’ll give you points!
Answer: Choice B) [tex]-4 \le x < 2[/tex]
Explanation:
The closed circle at the endpoint -4 means we'll include this value as part of the shaded solution set. In contrast, the endpoint 2 is not included because of the open hole here.
This graph is describing everything between -4 and 2, including -4 but excluding 2.
In other words, we can have x = -4 but can't have x = 2. Then we include everything in between those endpoints. So that's why we go for [tex]-4 \le x < 2[/tex]
Answer:
-4≤x<2
Step-by-step explanation:
-4 has a closed circle which means it is included in the less than or equal to and the 2 is less than x
Evaluate the function. f(x)=-3x^2 f(x)=−3x 2 \text{Find }f(-2) Find f(−2)
Answer:
12
Step-by-step explanation:
f(-2) = -3*(-2^2)
f(-2) = -3*-4
f(-2) = 12
Power Function:
Consider the following graphs (1 and 2), and answer the questions FOR EACH GRAPH:
A) In what interval of the graph is it increasing, decreasing and constant? This answer must be justified by means of the definition
B) What is the domain and range?
C) Is it an odd or even function? This answer must be justified by means of the definition
Graph 1
Part (a)
The function is increasing when x > 0. The function is decreasing when x < 0.
The function is never constant
An increasing portion is when the graph goes uphill when moving left to right. A decreasing portion goes in the opposite direction: it goes downhill when moving left to right.
The reason why the function is never constant is because there aren't any flat horizontal sections. Such sections are when x changes but y does not. No such sections occur.
------------------------
Graph 1
Part (b)
Domain = set of all real numbers
Range = set of y values such that [tex]y \ge 0[/tex]
The domain is the set of all real numbers because we can plug in any value for x without any restriction. There are no division by zero errors to worry about, or square roots of negative numbers to worry about either.
The range is the set of nonnegative numbers as the graph indicates. The lowest y gets is y = 0.
------------------------
Graph 1
Part (c)
The function is even
The function f(x) = 1.6x^12 is an even function due to the even number exponent. For any polynomial, as long as the exponents are all even, then the function itself is even. If all the exponents were odd, then the function would be odd. This applies to polynomials only. A power function is a specific type of polynomial.
Note in the graph, we have y axis symmetry. The mirror line is vertical and placed along the y axis. This is a visual trait of any even function.
We could use algebra to show that f(-x) = f(x) like so
f(x) = 1.6x^12
f(-x) = 1.6(-x)^12
f(-x) = 1.6x^12
The third step is possible because (-x)^12 = x^12 for all real numbers x. It's similar to how (-x)^2 = x^2. You could think of it like (-1)^2 = (1)^2
============================================================
Graph 2
Part (a)
The function is decreasing when x < 0 and when x > 0
The function is never increasing
The function is never constant
In other words, the function is decreasing over the entire domain (see part b). The only time it's not decreasing is when x = 0.
The function is decreasing because the curve is going downhill when moving to the right. You can think of it like a roller coaster of sorts.
At no point of this curve goes uphill when moving to the right. Therefore, it is never increasing. The same idea applies to flat horizontal sections, so there are no constant intervals either.
------------------------
Graph 2
Part (b)
Domain: x is any real number but [tex]x \ne 0[/tex]
Range: y is any real number but [tex]y \ne 0[/tex]
Explanation: If we tried plugging x = 0 into the function, we get a division by zero error. This doesn't happen with any other number. Therefore, the set of allowed inputs is any number but 0.
The range is a similar story. There's no way to get y = 0 as an output.
If we plugged y = 0 into the equation, then we'd get this
y = 17x^(-3)
0 = 17/(x^3)
There's no way to have the right hand side turn into 0. The numerator is 17 and won't change. Only the denominator changes. We can't have the denominator be 0.
------------------------
Graph 2
Part (c)
The function is odd
We can prove this by showing that f(-x) = -f(x)
f(x) = 17x^(-3)
f(-x) = 17(-x)^(-3)
f(-x) = 17* ( -(x)^(-3) )
f(-x) = -17x^(-3)
f(-x) = -f(x)
This is true for nearly all real numbers x, except we can't have x = 0.
Graphic 1:
(A) If f(x) = 1.6x ¹², then f '(x) = 19.2x ¹¹. Both f '(x) and x have the same sign, which means
• for -∞ < x < 0, we have f '(x) < 0, so that f(x) is decreasing on this interval
• for 0 < x < ∞, we have f '(x) > 0, so f(x) is increasing on this interval
f(x) is not constant anywhere on its domain.
(B) Speaking of domain, since f(x) is a polynomial (albeit only one term), it has
• a domain of all real numbers
• a range of {y ∈ ℝ : y = f(x) and y ≥ 0} (in other words, all real numbers y such that y = 1.6x ¹² and y is non-negative)
(C) This function is even, since
f(-x) = 1.6 (-x)¹² = (-1)¹² × 1.6x ¹² = 1.6x ¹² = f(x)
Graphic 2:
(A) Now if f(x) = 17/x ³, then f '(x) = -51/x ⁴. Because x ⁴ ≥ 0 for all x, this means f '(x) < 0 everywhere, except at x = 0. So f(x) is decreasing for (-∞ < x < 0) U (0 < x < ∞).
(B) f(x) has
• a domain of {x ∈ ℝ : x ≠ 0} (or all non-zero real numbers)
• a range of {y ∈ ℝ : y = f(x) and y ≠ 0} (also all non-zero reals)
(C) This function is odd:
f(-x) = 17/(-x)³ = 1/(-1)³ × 17/x ³ = -17/x ³ = -f(x)
Người ta chiếu xạ liều 3000 Rơn ghen vào một quần thể ruồi dấm ở thế hệ F1: Chiếu xạ 1000 con ruồi dấm không cho ăn đường thì có 80 con bị đột biến và chiếu xạ 1000 con ruồi dấm có cho ăn đường thì có 120 con bị đột biến. Cho ăn đường có ảnh hưởng đến tỉ lệ đột biến của ruồi giấm không, với mức ý nghĩa 5%? Giá trị kiểm định là
Answer:
gggggggggggggggggggggrrrrrrrrrrrttyuuiiiii
There are two types of fish in a lake. These are carp and pike.
In a netted area of the lake 120 carp and 16 pike were caught
In the whole lake it is estimated there are 34 000 fish.How many pike are there?
Answer:pike are 250 ; from 120+16=136 and 34000/136 is 250
Step-by-step explanation:
What is the length of the line?
What type of polynomial is: -2/3 b^3
Answer:
I think cubic polynomial cause degree is 3
What number when multiplied by itself is 11 greater than the preceding number when it is multiplied by itself
Answer: 5 and 6
Step-by-step explanation:
X^2 - 11 = (X-1)^2
X^2 - 11 = X^2-2X+1
X^2 - X^2 + 2X = 11+1
2X = 12
X = 6
The preceding number is 5
(6)(6)=36 and (5)(5)=25
36-25=11
The number required is 6
Let the number required bee xIf the number is multiplied by itself, it becomes x²
If the result is 11 greater than the preceding number when it is multiplied by itself is expressed as:
x² - 11 = (x - 1)²
x² - 11 = x² - 2x + 1
2x = 11 + 1
2x = 12
x = 6
Hence the number required is 6
Learn more on equation here: https://brainly.com/question/2972832
Geometry Identify the sides or angles that need to be congruent in order to make the given triangles congruent by AAS. Please help me!!!!!!!!!
Answer:
A. Sides AC and DF
B. Angles BAC and EDF
Answer:
Step-by-step explanation:
it takes Bert 30 minutes longer to mow a rectangular lawn that measures 30 feet by 25 feet than it takes him to mow a rectangular lawn that measures 20 feet by 15 feet. if he mows the two lawns at the same rate per square foot, how long does it take him to mow both lawns ?
A)50min
B)60min
C)70min
D)80min
Answer:
C: 70 Mins
Step-by-step explanation:
1, 20ft*15ft=300ft^2
2, 30ft*25ft=750ft^2
3, 750ft-350ft=450ft^2
4, 450 ft^2 = 30 mins
5, 350ft=750ft=1050ft^2
6, 1050/450=2.3333
7, 30*2.3333=70
8, 70 mins
At the same rate per square foot , Bert will take 80 minutes to mow the both lawns.
What is rate?Rate is the ratio between two related quantities in different units.
Area of the rectangular lawn = lw
where
l = lengthw = widtharea of the lawn1 = 30 × 25 = 750 ft²
area of the lawn2 = 20 × 15 = 300 ft²
Therefore,
He mow the firts lawn 30 minutes longer than the second lawn. Therefore,
let
x = time to mow the second lawn
x + 30 = time to mow the first lawn
rate for the first lawn = 30 + x / 750
rate for the second lawn = x / 300
Hence,
30 + x / 750 = x / 300
cross multiply
9000 + 300x = 750x
9000 = 750x - 300x
9000 = 450x
x = 9000 / 450
x = 20
it will take him 30 + 20 + 20 = 80 minutes to mow the both lawns.
learn more on rate here: https://brainly.com/question/5219196
Which of the following options correctly represents the complete factored
form of the polynomial F(x) = x^3- x2 - 4x-6?
A. F(x) - (x - 3)(x + 1 + I)(x+1- I)
B. F(x) = (x - 3)(x+1+I)(x-1-I)
C. F(x) = (x+3)(x + 1)(x - 1)
D. F(x) - (x+3)(x+1+I)(x +1-I )
The completely factored form for the given algebraic expression is f(x) = (x-3)(x+1+i)(x+1-i).
What is a completely factored polynomial?A completely factored polynomial is a polynomial that can no longer be further simplified. A completely factored polynomial can be expressed as a root of its own equation.
Given that:
f(x) = x³ - x² - 4x - 6
To express this as a factored polynomial using the rational:
f(x) = (x-3)(x²+2x+2)
f(x) = (x-3)(x+1+i)(x+1-i)
Learn more about how to completely factor polynomial here:
https://brainly.com/question/11434122
#SPJ1
plz help brainliest to correct answer
Answer:
-2 would be right next to -3 because its negative and -1 would be right next to -2, 2 would be two points away from 0 bc its a whole number
What is the derivative of 5x^4+4?
Answer:
[tex]\displaystyle \frac{dy}{dx} = 20x^3[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = 5x^4 + 4[/tex]
Step 2: Differentiate
Derivative Property [Addition/Subtraction]: [tex]\displaystyle y' = \frac{d}{dx}[5x^4] + \frac{d}{dx}[4][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle y' = 5\frac{d}{dx}[x^4] + \frac{d}{dx}[4][/tex]Basic Power Rule: [tex]\displaystyle y' = 20x^3[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
