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 29E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 29E

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

Explanation of Solution

Given:

The given function is y=sin(tan2x) .

Calculation:

  y=sin(tan2x)

Apply chain rule.

  df(a)dx=dfdadadx

Let f=sin(a),a=tan(2x)

  dydx=dda(sina)ddx(tan2x)

Use derivative rule.

  ddx(sinx)=cosxandddx(tanx)=sec2x .

  dydx=cos(a)sec2(2x)2dydx=2cos(a)sec2(2x)

Substitute the value of a=tan(2x) .

  dydx=2cos(tan(2x))sec2(2x)

Hence the derivativeof the given function is dydx=2cos(tan(2x))sec2(2x) .

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