BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.4, Problem 32E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 32E

The derivative of the given function is dydx=2cos(tan(2x))sec2(2x) .

Explanation of Solution

Given:

The given function is y=sin(sin(sinx)) .

Calculation:

  y=sin(sin(sinx))

Apply chain rule.

  df(a)dx=dfdadadx

Let f=sin(a),a=sin(sinx)

  dydx=dda(sina)ddx(sin(sinx))

Use derivative rule.

  ddx(sinx)=cosx .

  dydx=cosaddx(sin(sinx))

Substitute the value of a=sin(sinx) .

  dydx=cos(sin(sinx))ddx(sin(sinx))

Apply chain rule.

  df(a)dx=dfdadadx

Let f=sin(a),a=sinx

  dydx=cos(sin(sinx))dda(sina)ddx(sinx)

Use derivative rule.

  ddx(sinx)=cosx .

  dydx=cos(sin(sinx))cosacosx

Substitute the value of a=sinx .

  dydx=cos(sin(sinx))cos(sinx)cosx

Hence the derivativeof the given function is dydx=cos(sin(sinx))cos(sinx)cosx .

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