Answer:
[tex] \rm \displaystyle y' = 2 {e}^{2x} + \frac{1}{x} {e}^{2x} + 2 \ln(x) {e}^{2x} [/tex]
Step-by-step explanation:
we would like to figure out the differential coefficient of [tex]e^{2x}(1+\ln(x))[/tex]
remember that,
the differential coefficient of a function y is what is now called its derivative y', therefore let,
[tex] \displaystyle y = {e}^{2x} \cdot (1 + \ln(x) )[/tex]
to do so distribute:
[tex] \displaystyle y = {e}^{2x} + \ln(x) \cdot {e}^{2x} [/tex]
take derivative in both sides which yields:
[tex] \displaystyle y' = \frac{d}{dx} ( {e}^{2x} + \ln(x) \cdot {e}^{2x} )[/tex]
by sum derivation rule we acquire:
[tex] \rm \displaystyle y' = \frac{d}{dx} {e}^{2x} + \frac{d}{dx} \ln(x) \cdot {e}^{2x} [/tex]
Part-A: differentiating $e^{2x}$
[tex] \displaystyle \frac{d}{dx} {e}^{2x} [/tex]
the rule of composite function derivation is given by:
[tex] \rm\displaystyle \frac{d}{dx} f(g(x)) = \frac{d}{dg} f(g(x)) \times \frac{d}{dx} g(x)[/tex]
so let g(x) [2x] be u and transform it:
[tex] \displaystyle \frac{d}{du} {e}^{u} \cdot \frac{d}{dx} 2x[/tex]
differentiate:
[tex] \displaystyle {e}^{u} \cdot 2[/tex]
substitute back:
[tex] \displaystyle \boxed{2{e}^{2x} }[/tex]
Part-B: differentiating ln(x)•e^2x
Product rule of differentiating is given by:
[tex] \displaystyle \frac{d}{dx} f(x) \cdot g(x) = f'(x)g(x) + f(x)g'(x)[/tex]
let
[tex]f(x) \implies \ln(x) [/tex][tex]g(x) \implies {e}^{2x} [/tex]substitute
[tex] \rm\displaystyle \frac{d}{dx} \ln(x) \cdot {e}^{2x} = \frac{d}{dx}( \ln(x) ) {e}^{2x} + \ln(x) \frac{d}{dx} {e}^{2x} [/tex]
differentiate:
[tex] \rm\displaystyle \frac{d}{dx} \ln(x) \cdot {e}^{2x} = \boxed{\frac{1}{x} {e}^{2x} + 2\ln(x) {e}^{2x} }[/tex]
Final part:
substitute what we got:
[tex] \rm \displaystyle y' = \boxed{2 {e}^{2x} + \frac{1}{x} {e}^{2x} + 2 \ln(x) {e}^{2x} }[/tex]
and we're done!
Answer:
Product Rule for Differentiation
[tex]\textsf{If }y=uv[/tex]
[tex]\dfrac{dy}{dx}=u\dfrac{dv}{dx}+v\dfrac{du}{dx}[/tex]
Given equation:
[tex]y=e^{2x}(1+\ln x)[/tex]
Define the variables:
[tex]\textsf{Let }u=e^{2x} \implies \dfrac{du}{dx}=2e^{2x}[/tex]
[tex]\textsf{Let }v=1+\ln x \implies \dfrac{dv}{dx}=\dfrac{1}{x}[/tex]
Therefore:
[tex]\begin{aligned}\dfrac{dy}{dx} & =u\dfrac{dv}{dx}+v\dfrac{du}{dx}\\\\\implies \dfrac{dy}{dx} & =e^{2x} \cdot \dfrac{1}{x}+(1+\ln x) \cdot 2e^{2x}\\\\& = \dfrac{e^{2x}}{x}+2e^{2x}(1+\ln x)\\\\ & = \dfrac{e^{2x}}{x}+2e^{2x}+2e^{2x} \ln x\\\\& = e^{2x}\left(\dfrac{1}{x}+2+2 \ln x \right)\end{aligned}[/tex]
Which best describes the relationship between the line that passes through the points (-6,5) and (-
2,7) and the line that passes through the points (4, 2) and (6, 6)?
Answer:
Slope passes through (-6, 5) and (-2, 7)
[tex]m_1=\frac{y_2-y_1}{x_2-x_1} =m_1=\frac{7-5}{-2+6}[/tex]
[tex]m_1=\frac{2}{4} =\frac{1}{2}[/tex]
Slope passes through (4, 2) and (6, 6)
[tex]m_2=\frac{6-2}{6-4}[/tex]
[tex]\frac{4}{2} =2[/tex]
[tex]m_1\times m_2 \neq -1[/tex] [tex]m_1\neq m_2[/tex]
Answer:- A) neither perpendicular nor parallel.
OAmalOHopeO
Analyze the key features of the graph of the quadratic function f(x) = –x^2 + 4x – 3.
1. Does the parabola open up or down?
2. Is the vertex a minimum or a maximum?
3. Identify the axis of symmetry, vertex and the y-intercept of the parabola.
9514 1404 393
Answer:
downmaximumx=2; (2, 1), -3Step-by-step explanation:
1. The negative leading coefficient (-2) tells you the parabola opens downward.
__
2. The fact that the parabola opens downward tells you the vertex is a maximum.
__
3. For quadratic ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For this parabola, that is x = -4/(2(-1)) = 2. The y-value of the vertex is f(2) = -2^2+4(2)-3 = -4+8-3 = 1. The y-intercept is the constant, c = -3.
axis of symmetry: x = 2vertex: (2, 1)y-intercept: (0, -3)Solve for X
(Ignore the math I did on top)
Help me plz will mark brainliest
Step-by-step explanation:
Given,
the bigger triangle (∆GFH), <HGF = 90° and <GFH = 60° and GF = 4
In the 30-60-90 triangle, FH = 4×2 = 8
or you can find it like this,
cos60 = 4/FH
FH = 4/cos60 = 8
Now, I is the midpoint of FH, so, FI = 8/2 = 4
now for ∆FGI,
<GFI = 60°, GF = 4, FI = 4, it's a equilateral triangle, so we can say GI = 4
Now we need to find the height of ∆FGI, for that,
area of ∆FGI = (√3/4)×4² = 4√3 = 6.92820323..
So height (GJ) = 2×area/side = 2×4√3/4 = 2√3 = 3.46410162.. [height of ∆GFI (Because altitude is perpendicular distance from a point) = GJ, given]
now, in ∆GJI, GJ = 2√3, GI = 4 and <GJI = 90° (since itsy altitude, the angle will be a right angle, i.e. 90°)
So, JI = √{4²-(2√3)²} = 2
Area = 2×2√3/2 = 2√3 = 3.46410162.. = 3.46 (rounded to the nearest hundredth)
Two numbers are in the ratio 2:3. If 3 is added to the numbers, the ratio changes to 3:4. Find the numbers.
Answer:
6:9
Step-by-step explanation:
Answer:
6 and 9
Step-by-step explanation:
according to the question, the nos. are 2x and 3x.
then, (2x+3)/(3x+3)=3/4
therefore, 4(2x+3)=3(3x+3)
8x+12=9x+9
12-9=9x-8x
3=x
therefore the nos. are 2×3=6 & 3×3=9
Answer from Gauth math
Help due today
No links
Answer:
-6
Step-by-step explanation:
Answer:
[tex]24 + x = 13 \\ x = 13 - 24 \\ x = - 11 \\ thank \: you[/tex]
If anyone can help me I will really appreciate!!
Answer:
The decimal form of the equation is y = 2.5x + 10
The equivalent fraction form is y = (5/2)x + 10 because 5/2 = 2.5
===========================================================
Explanation:
We can pick any two columns from the table to form the two points needed.
I'll pick the first two columns
(1, 12.5)
(2, 15)
Then apply the slope formula to those points
m = (y2-y1)/(x2-x1)
m = (15-12.5)/(2-1)
m = (2.5)/(1)
m = 2.5
Now use that slope with either point mentioned to find the y intercept b.
y = mx+b
12.5 = 2.5*1 + b
12.5 = 2.5 + b
12.5 - 2.5 = b
10 = b
b = 10
Or
y = mx+b
15 = 2.5*2+b
15 = 5+b
15-5 = b
10 = b
b = 10
We end up with the same b value.
We found that m = 2.5 is the slope and b = 10 is the y intercept
Therefore we go from y = mx+b to y = 2.5x + 10
This is the same as saying y = (5/2)x + 10 since 2.5 = 5/2
Last month, a printing company printed $56,000.00 worth of books. This month, they printed $63,000.00 worth of books. What is the percent increase in their printing?
Select the expression that represents the following statement: 3 times one fourth the difference of 26 and 10.
one fourth x (26 + 10) x 3
one fourth x (26 − 10) x 3
3 x one fourth x 26 − 10
3 x one fourth x 26 x 10
PLEASEE HEPPP
Answer:
the second option #2
one fourth x (26-10) x 3
Step-by-step explanation:
Two of the options (#1 and #4) can be ruled out immediately since they don't involve the difference of 26 and 10.
#3 can be ruled out because the difference needs to be multiplied by one fourth, but this option gives the wrong answer since the multiplication is done before subtraction (BODMAS)
Answer:
c
Step-by-step explanation:
I got it correct on a quiz
-1/3 + -3/8 | pls include instructions/step by step! thx!
[tex]\\ \sf\longmapsto \dfrac{-1}{3}+(\dfrac{-3}{8})[/tex]
Take lcm[tex]\\ \sf\longmapsto \dfrac{-8+(-9)}{24}[/tex]
[tex]\\ \sf\longmapsto \dfrac{-8-9}{24}[/tex]
[tex]\\ \sf\longmapsto \dfrac{-17}{24}[/tex]
-1/3 + -3/8
denominator: -1/3 * 8
-3/8 * 3
<=> -8/24 + - 9/24
<=> (-8 + -9)/24
= -17/24
Milo receives a commission of 4% on all sales. If his commission on a sale was $51.00 , find the cost of the item he sold.
Answer:
1275
Step-by-step explanation:
51.00 = x*.04
51/.04 = 1275
Answer:
Step-by-step explanation:
4% x = 51
4/100 * x = 51 Multiply both sides by 100
100 * 4/100 * x = 5100
4x = 5100 Divide by 4
x = 5100/4
x = 1275
I didn't believe it was that large. Give the other answerer the Brainlest.
Find the value of x.
A. 86
B. 172
C. 94
D. 188
Answer:
188
Step-by-step explanation:
Tangent Chord Angle = 1/2Intercepted Arc
94 = 1/2 x
Multiply by 2
2*94 =x
188 =x
Multiply and simplify the following complex numbers (-4-5i)•(1-i)
Answer:
Step-by-step explanation:
(-4 - 5i)⋅(1 - i) = (-4)(1) + (-4)(-i) + (-5i)(1) + (-5i)(-i)
= -4 + 4i - 5i + 5i²
= -4 - i -5
= -9 - i
John is tall Paul is taller but Ken is the tallest. Who is the shortest?Who is the tallest?
Answer:
Shortest is john
Tallest is ken
Step-by-step explanation:
You have to look at the last few words (er, est).
Ex: 3. strong 2. stronger 1. strongest
Hope this helps <3
Need thanks? Comment /hearthelp
6 x ____ = 9
6 times what number equals 9
Answer:
3/2
Step-by-step explanation:
6 * _x___ = 9
Divide each side by 6
6 x __x__ = 9
x = 9/6
Simplify
x = 3/2
Answer:
1.5
Step-by-step explanation:
Well, in this form you'd multiply 1 and .5 by 6 separately and then add them together. This makes 1*6 = 6 and 0.5*6=3, add them together and you get 9.
Combine like terms to simplify the
equation below.
Answer:
4a+6b
Step-by-step explanation:
4a -2a +6b +2a
Combine like terms
4a-2a+2a+6b
4a+6b
Answer:
4a + 6b
Step-by-step explanation:
4a - 2a + 6b + 2a
= 4a + 6b
(because -2a and +2a get cancelled by each other)
first off thanks to the ppl who answered before 2nd off i need help again
Answer:
This number line show the inequality x > 2
Question
Tony has only $20 bills and $5 bills in his wallet. If he has 12 bills that add up to a total of $210, how many of each type of
bill does Tony have?
Answer:
10 $20 dollar bills, and 2 $5 dollar bills
Really, you could say that he has 9 twenties, and 4 fives, but that would be impractical.
can somone heelp me
m
Answer:
b
Step-by-step explanation:
Suggest that you and your boss schedule regular check-ins at lunchtime and at the end of the day
Keep smiling and have a nice day :)
For the inequality 4 < -x^2– y, where is the graph shaded and is the curve solid or dotted"
answer=
X<-4
.............................................................
Solve for theta
Please answer both parts
Answer:
Step-by-step explanation:
a) tanθ = x/3
θ = arctan(x/3)
:::::
b) cosθ = 9/x
θ = arccos(9/x)
please help answer question
Answer:
Mark me brainlist please please please please
Answer:
Step-by-step explanation:
please solve asap thanks
I think..
A' =( -1,-4 )
B' = ( 3,-2 )
C'=( - 2, 2 )
Answer:
A' (-3, 12)
B' (9, 6)
C' (-6, -6)
Step-by-step explanation:
A (-1 , 4 ) , K = 3 => K * each with coordinate of A => (-1 * 3, 4 * 3)
B ( 3 , 2 ) , K = 3 => K * each with coordinate of B => (3 * 3, 2 * 3)
C ( -2 , -2 ) , K = 3 => K * each with coordinate of C => (-2 * 3, -2 * 3)
help with 5 please( question tuped below too).
Prove that y=x+2 is a tangent to the locous P(2t²,4t).
find the point of contact of this tangent to this locous and hence find the equation of normal at the point.
thanks
9514 1404 393
Answer:
tangent point: (2, 4)normal: y = -x +6Step-by-step explanation:
The derivative of P with respect to t is ...
P' = (x', y') = (4t, 4)
so the slope of the curve for some value of t is ...
dy/dx = y'/x' = 4/(4t) = 1/t
The line we want to be a tangent is y = x +2, which has a slope of 1. The curve will have a slope of 1 where ...
1/t = 1 ⇒ t = 1
At t=1, the point P is (2·1², 4·1) = (2, 4). For x=2, the point on the desired tangent is y = x +2 = 2 +2 = 4, or (x, y) = (2, 4).
The curve and the given line both have a slope of 1 at the point (2, 4), so that is the tangent point.
__
The normal to the curve at (2, 4) will have a slope that is the opposite reciprocal of the slope of the tangent: -1/1 = -1. Then point-slope form of the equation of the normal line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -4 = -1(x -2) . . . . . . line with slope -1 through point (2, 4)
y = -x +6 . . . . . . . . equation of the normal line in slope-intercept form
If x+y=8 and xy =15 find the value of x³+y³.
Answer:
152Step-by-step explanation:
let x= 5 and y= 3x + y = 85 + 3 = 8xy = 155 × 3 = 15x³ + y³ = ?5³ + 3³ = ?125 + 27 = 152[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
The count in a bacteria culture was 900 after 15 minutes and 1100 after 35 minutes. Assuming the count grows exponentially,
What was the initial size of the culture?
Answer:
300
Step-by-step explanation:
1100 = 900 [tex]e^{k*20}[/tex]
1.222222 = [tex]e^{k*20}[/tex]
ln(1.222) = 20k ln(e)
k = ln(1.222)/20
k = .2004
900 = x [tex]e^{15* .20004}[/tex]
900/x = [tex]e^{15* .20004}[/tex]
[tex]e^{15*.2004} = 900/x[/tex]
x = 900/ [tex]e^{15*.2004}[/tex]
x = 300
Which shapes are quadrilaterals?
1. Scalene right triangle
2. Obtuse scalene triangle
3. Isosceles right triangle
4. Hexagon
5. Pentagon
6. Right trapezoid
7. Venn diagram
Hey there! I'm happy to help!
A quadrilateral is any polygon (enclosed shape) with four sides. Let's see what each of these shapes are.
Scalene right triangle - the prefix tri- means three (tricycle, tripod, triple, etc.), and all triangles have three sides, so this is not a quadrilateral.Obtuse scalene triangle - once again a triangle, so not a quadrilateral.Isosceles right triangle - would you look at that, another triangle! Not a quadrilateral.Hexagon - a hexagon is a six-sided polygon (hex=six), so this is not a quadrilateral.Pentagon - a pentagon is a five-sided polygon (pent=five, like Pentatonix!). Not a quadrilateralRight trapezoid - a trapezoid is a quadrilateral with at least one pair of parallel sides!Venn diagram - a Venn diagram is a compare and contrast chart made of two overlapping circles (ZERO sides), so this is not a quadrilateral.So, the only shape on your list that is a quadrilateral is 6. right trapezoid.
Have a wonderful day! :D
2+2 what is da answer ill gib bralniest
Answer:
4
Step-by-step explanation:
2+2=4
Answer:
Step-by-step explanation:
4
Rewrite 3.16 as a fraction (the 6 is repeating)c
[tex]3\frac{16}{99} = \dfrac{313}{99}= 3.161616161616.....[/tex]
I need help with 4 x (7 - 3) please show your work
Answer: 16
Step-by-step explanation:
Take ( 7 - 3 ) and subtract 3 from 7, which gives you 4, then take 4 and multiply it by 4, ( 4x4 ) which gives you 16.
Answer:
16
Step-by-step explanation:
4 * (7 - 3)
Parentheses first
4*(4)
Then multiply
16
