Question: Ify = sin(x7),then the outer function is the sine function and the inner function is the power function, so the Chain Rule gives the following.dydx=ddxsin(x7)=cos(x7)outerevaluatedderivativeevaluatedderivativefunctionat

Ify = sin(x7),then the outer function is the sine function and the inner function is the power function, so the Chain Rule gives the following.dydx=ddxsin(x7)=cos(x7)outerevaluatedderivativeevaluatedderivativefunctionat innerof outerat innerof innerfunctionfunctionfunctionfunction=.(b)Note thatsin7(x)=(sin(x)).Here the outer function is the power function and the inner function is the sine function. Sodydx=ddx(sin(x))7=7(sin(x))6innerderivative of outerderivativefunctionfunction evaluated of innerat inner functionfunction=.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Differentiate the following. (a) y = sin(x4) (b) y = sin*(x) Solution (a) If y = sin(x*), then the outer function is the sine function and the inner function is the power function, so the Chain Rule...

\fDifferentiate the following. (a) y = sin(x4) (b) y = sin*(x) Solution (a) If y = sin(x*), then the outer function is the sine function and the inner function is the power function, so the Chain...

1. If f(x) = sin (x), find f' a. 0 C. b. 1 d. 2. If f(x) = sin X COS X a. 1 C. b. -2 d. 2 3. Find the slope of the tangent to the curve y = 2 sin x at x = = a. C. -1 b. 3 d. -3 4. Find the slope of...

AP Calculus Unit 3 Test (Please show your work) 1. Find ify = (In x) 4 2. Find ~ at (1,3) if y = Vx2 + 8x 3. Find if y = sin (tan 2x) 4. Find ify =" Int 12 5. Find the equation of the tangent line to...

Need solutions 1. If f(x) = sin (x), find f a. 0 C. b. 1 d. 2. If f(x) = Sin X find f * COS X a. 1 C. b. -2 d. 2 3. Find the slope of the tangent to the curve y = 2 sin'x at x = a. C. -1 b. 3 d. 4....

Answer questions 1-32 True/False Indicate whether the statement is true or false. 1. The quotient rule can be used to differentiate a rational function. 2. The slope of a tangent to a curve is found...

AP Calculus Unit 3 Test (Please show your work) 1. Find ify = (In x) 4 2. Find - at (1,3) if y = Vx2 + 8x 3. Find ify = sin (tan 2x) 4. Find ify = In t 5. Find the equation of the tangent line to the...

9 10 Question * (2 Points) Question * (2 Points) Find y' if x = 2Arcsin 2t; y = 4Arccos 2t. (A) -2 ( c ) 2t Find y' if y = In 73x-4) (B ) -t A (2)(3x-8) (x) (3x-4) 4x3 (24)(x-3) (3)(3x-4) ( B...

7. If y = 2 sinx - cos x, find y" at * = a. 1 + 13 C. 1- 2-53 b. 1 - 13 2 d. 1+213 2 8. Ify = - sin 3x , find y" at x = . a. 1 b. -1 d. $2 9. Find the slope of the tangent to y = 1 - 2 sin x at the...

Multiple Choice Identify the choice that best completes the statement or answers the question. 11. Evaluate the limit, if it exists: lim 25-x 2 345 X-5 a. 10 C. 0 b. -10 d. does not exist12. Evaluate...

A company is issuing a 3-year maturity bond that is expected to pay $40 every six month and a lump sum of $1000 at the end of three years from now. If bond investors require 5% annual nominal...

Redford is a seller of electric generators. He purchases a large quantity of generators from a manufacturer, Mallon Corp., by making a down payment and signing an agreement to make the balance of...

GASB standards require that general capital assets be recorded in the fund statements at: Multiple Choice None of the options are correct. Estimated cost at the financial statement date. Fair value...

Your clients have asked you about being able to deduct investment interest during 2019. They took out a loan to purchase a commercial lot that they will hold for investment and plan on selling in a...