Find from first principles the derivative of cos x​

Answers

Answer 1

Answer:

Please see the explanation.

Step-by-step explanation:

Let

[tex]f\left(x\right)=cosx[/tex]

By the first principle

[tex]f\:'\left(x\right)=\lim _{h\to 0}\left(\frac{f\left(x+h\right)-f\left(x\right)}{h}\right)[/tex]

          [tex]=\lim _{h\to 0}\left(\frac{cos\:\left(x+h\right)-cos\:x}{h}\right)[/tex]

           [tex]=\lim _{h\to 0}\left[\frac{cos\:x\:cos\:h-sin\:x\:sin\:h\:-\:cos\:x}{h}\right][/tex]

           [tex]=\lim _{h\to 0}\left[\frac{-cos\:x\left(1-cos\:h\right)-sin\:x\:sin\:h\:}{h}\right][/tex]

           [tex]=\lim _{h\to 0}\left[\frac{-cos\:x\left(1-cos\:h\right)\:}{h}-\frac{sin\:x\:sin\:h}{h}\right][/tex]

           [tex]=-cosx\:\left(\lim \:_{h\to \:0\:}\frac{1-cos\:h}{h}\right)-sin\:x\:\lim \:\:_{h\to \:\:0}\:\left(\frac{sin\:h}{h}\right)[/tex]

           [tex]=-cosx\:\left(0\right)-sinx\left(1\right)[/tex]

            [tex]=-sin\:x[/tex]


Related Questions

length A is 4 ft. after a dilation is performed length B is 7ft. what was the scale factor used?

Answers

1.75

4 x 1.75 = 7 so that is the answer

The Smith family went out to dinner and received great service. They decided to
leave a 20% tip for their waitress. If their dinner bil totaled $90, how much was the
tip? Think You need to find what percent of what number? Show your work

Answers

Answer:

$75

Step-by-step explanation:

90=1.2x

90/1.2=x

75=x

Answer:

$75 :D

Step-by-step explanation:

90=1.2x 90/1.2=x 75=x

can 15/55 be simplified. and if so what would it be?​

Answers

Answer: [tex]\frac{3}{11}[/tex]

Step-by-step explanation:

This number can definitely be simplified by five.

= [tex]\frac{15}{55}[/tex] ÷ [tex]\frac{5}{5}[/tex]

= [tex]\frac{3}{11}[/tex]

Hope this helps! :D

Someone plis help me with this homework

Answers

Answer:

True

Step-by-step explanation:

The diagram shows a triangle PST and a parallelogram PQRS.

EASY MATH QUESTION PLS HELP!!!
Which of the following values is a solution for the inequality statement?
Select all that apply.

Answers

Answer:

-150, 55, -78

Step-by-step explanation:

44>a-64

108>a

HELPHELPHELPHELPHELP

Answers

E, C, B

When you solve the equation for y, the slope (number next to x) should be 3, because In order for it to be parallel to the original line they need to have the same slope

please answer this for me I need it it's due at midnight

Answers

i’m pretty sure that’s C

Pierre correctly simplified an expression. When he substituted x = 2 into the simplified expression, the value was 20. Which could be Pierre’s original expression?
2(7x – 4)
2(x – 19)
2(x + 10)
2(5x + 1)

Answers

Answer:2(7x-4)

Step-by-step explanation:

Answer:

The correct answer is A.) 2(7x – 4)

Step-by-step explanation:

I just did the test and got it right

solve the equation for w. x=w/a

Answers

Answer:

w=xa

Step-by-step explanation:

Rewrite the equation as w/a=x

w/a=x

Multiply both sides of the equation by a

w=x*(a)

Multiply x by a

w=xa

Hope this helped!

can someone pls help me?

Answers

Answer:

yes, every one will fit.

Step-by-step explanation:

114 divided by 3 is 38 so there are 38 teams and each person will fit.

9514 1404 393

Answer:

  22.  yes

  23.   is divisible by 9

Step-by-step explanation:

A number is divisible by 9 if the sum of its digits is divisible by 9. The process of reducing the sum of digits to a single digit is called "casting out nines." It can be a useful process for checking arithmetic of all sorts.

A number is divisible by 3 if the sum of its digits is divisible by 3.

__

22. 114 is divisible by 3 because 1+1+4 = 6, a number divisible by 3. Everyone will have a spot.

__

24. 2187 has a sum of digits of 2+1+8+7 = 18, which has a sum of digits of 1+8=9. This is divisible by 9, so 2187 is divisible by 9.

5 points
A gym charges a $50 fee plus $20 per month. Another gym charges a fee
of $500. How many months will it take for the charges at the first gym to
reach $500? *

A 020 months
B 5.5 months
C 022.5 months
D 22 months

Answers

Step-by-step explanation:

it so easy bro 5.5 ok bro.

What is -10 plus 9 ?

Answers

Answer:

-1

Step-by-step explanation:

-1 because -10 + 9 leaves u with one negative left

I NEED A GOOD ANWSER
How many 6 inch photos will fit inside 48 inches?
(please write your answer and explain.

Answers

Answer:

8

Step-by-step explanation:

48/6 = 8

If this is what the question is asking.. just divide the space by the size of photos

In the figure below, o ll m. Find the values of y and z

Answers

Answer: y = 117 and z = 32

Step-by-step explanation:

y: 180 - 63 = 117

z: 180 - 117 (also known as y) = 63 which is the top corner right next to the equation for z, so you do it again. 180 - 63 = 117

then you do 117 + 43 = 160, then 160 divided by 5 = 32

which means that 5(32) - 43 = 117, 5 x 32 = 160 - 43 = 117.

hope this helps

CAN SOMEONE PLEASE HELP ME ASAP

Answers

Answer:

i think x would be 15

Step-by-step explanation:

A man had a piece of leather that was 34 metre long. He cut off 25 metre for a project and then cut off a 30-centimetre piece to give to his friend. What fraction of the original piece of leather is left? How many centimeters of the leather is left?

Answers

Answer:

8.7 meters left or 870 cm left

0.256 is fraction... 87/340

Step-by-step explanation:

34-25-0.3=8.7          8.7 x 100=870 cm

Tanyas baked goods took in 175$ To help raise money for the chorus club .Tanya need to spend 32$ for baking supplies write and evaluate and addition expression to find how much profit tanyas baked goods make ?

Answers

Step-by-step explanation:

6 I think that is the answer I hop you get it right

WHOLE NUMBERS AND INTEGERS
Identifying a sum as a point located a given distance from...
The number 5 is plotted on the number line below.
10
Answer the following questions.
(a) Which is a point 3 units to the right of 5 ?
5+(-3)
5+(-3)
O-5+3
5+3
(b) Which is a point 3 units to the left of 5 ?
S (3)
5+(-3)
0 5+3
5+3

Answers

Answer:

a) Point to the right: you need to add

5 + 3

Last option

b) Point to the left: you need to subtract or  add negative

5 + (-3)

First option

Solve for x to the nearest degree.

A 72
B 71
C 18
D 19

Answers

C18 dije djdjrjjrr disidiré djejurjrr eneiekjeje ewkkeksjeie amáñenme me
The answers 19 for this equation

I’ll give brainliest (plz asap)

Answers

Answer:

it's 3/10

Step-by-step explanation:

you would have to multiply all of those fraction so:

3/4 x 4/5 x 1/2=  3/10

i am so so sorry if i am wrong

Remy has $150 to spend on party supplies. She spends $75.50 on decorations and various other supplies. She spent the remaining money to order invitations. If she invited 20 people to her party, how much was the cost to print each invitation?

Answers

Answer:

the cost to price of each invitation is $3.725

Step-by-step explanation:

Given that

On party supplies she incurred $150

For decorations and various other supplies she incurred $75.50

The remaining amount i.e.

= $150 - $75.50

= $74.50

This amount would be incurred for the invitations

Now she invited 20 people

SO the cost to price of each invitation is

= $74.50 ÷ 20 people

= $3.725

Hence, the cost to price of each invitation is $3.725

Last year, the average cost of a computer was $730. This year, the cost has decreased by 10%. What is the average cost of a computer this year?

Answers

Answer:

657

Step-by-step explanation:

What is the value of X in this triangle?

Answers

Answer:

x = 3

Step-by-step explanation:

An equilateral ∆ has equal side lengths and all its angles are also equal to each other, which are 60° each.

The ∆ given has equal side lengths. Therefore it is an equilateral ∆ having equal angles, each would measure 60°.

Thus:

(25x - 15) = 60°

Solve for x

25x - 15 = 60

Add 16 to both sides

25x - 15 + 15 = 60 + 15

25x = 75

Divide both sides by 25

25x/25 = 75/25

x = 3

find the difference (20m+3)-(7m-5)

Answers

Answer:

Simplifying

(20m + 3) + -1(7m + -5) = 0

Reorder the terms:

(3 + 20m) + -1(7m + -5) = 0

Remove parenthesis around (3 + 20m)

3 + 20m + -1(7m + -5) = 0

Reorder the terms:

3 + 20m + -1(-5 + 7m) = 0

3 + 20m + (-5 * -1 + 7m * -1) = 0

3 + 20m + (5 + -7m) = 0

Reorder the terms:

3 + 5 + 20m + -7m = 0

Combine like terms: 3 + 5 = 8

8 + 20m + -7m = 0

Combine like terms: 20m + -7m = 13m

8 + 13m = 0

Solving

8 + 13m = 0

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-8' to each side of the equation.

8 + -8 + 13m = 0 + -8

Combine like terms: 8 + -8 = 0

0 + 13m = 0 + -8

13m = 0 + -8

Combine like terms: 0 + -8 = -8

13m = -8

Divide each side by '13'.

m = -0.6153846154

Simplifying

m = -0.6153846154Step-by-step explanation:

Answer:

(20m+3)-(7m-5).

(20m-7m)+(3+5).

13m(8). =104m

104m is your anwser! Hope this helps!

What should I choose

Answers

Answer:

Orange juice.

Step-by-step explanation:

It's the best thing ever it always gets u an A+ when you give it to your teachers

Answer:

variables

Step-by-step explanation:

Hope this helped, Have a Great Day!!

The price of a cup of coffee was 2.30 yesterday. Today, the price fell to 2.15 . Find the percentage decrease. Round your answer to the nearest tenth of a percent.

Answers

Answer:

6.5%

Step-by-step explanation:

Percentage decrease

[tex] = \frac{2.30 - 2.15}{2.30} \times 100 \\ \\ = \frac{0.15}{2.30} \times 100 \\ \\ = \frac{15}{2.30}\\ \\ = \frac{150}{23}\\ \\ = 6.52173913 \\ \\ \approx \: 6.5\%[/tex]

find the radius given the linear speed and rate of rotation v=24.8m/s, 120 rev/mins

Answers

Answer:

I got you Fam

Step-by-step explanation:

The radius is 12.4 meters if the linear speed and rate of rotation v=24.8m/s, 120 rev/mins.

What is angular acceleration?

It is defined as the rate of change in angular velocity with respect to time. It is also known as rotational acceleration.

It is given that:

The rate of rotation v = 24.8 m/s

The angular velocity w = 120 rev/mins

In rev/second

The angular velocity w = (120/60) rev/second = 2 rev/sec

The formula:

v = rw

Here r is the radius

r = v/w

r = 24.8/2

r = 12.4 meters

Thus, the radius is 12.4 meters if the linear speed and rate of rotation v=24.8m/s, 120 rev/mins.

Learn more about angular acceleration here:

https://brainly.com/question/13723307

#SPJ2


(12) - (23 +131) =
Express your answer in the form (a + bi),

Answers

Answer:

-142

Step-by-step explanation:

First solve parenthesis,

(12) - (23 +131) =

(12) -154

Finally subtract,

12-154

= -142

What is Three-fourths divided by one-sixth?

Answers

Answer:

18/4 or 9/2 or 4 1/2

Step-by-step explanation:

Answer:

9/2 or 4 1/2

Step-by-step explanation:

find the common denominator and divide across.

Need help! only have today till I turn in!

Answers

Answer:

yes

Step-by-step explanation:

(y1-y2)/(x1-x2)=(10-6)/(8-0) OR (6-10)/(0-8)
= 0.5
In that case you now know. The answer to the first blank (coefficient of x)
To find the y intercept (the second blank), which I will call c, you can use either pair of the coordinates and substitute them in the equation together with the gradient you found previously.
If you choose to sub in (0,6) and since gradient=0.5,
Then: 6=0.5(0) + c
therefore, c=6
Likewise, if you choose to sub in (8,10)
Then: 10=0.5(8) + c
Therefore, c also equals to 6
So in conclusion the gradient of the slop is 0.5 and the y intercept is 6
The linear function will be: y=0.5x + 6
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