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 3.3, Problem 13E
To determine

Find the differentiate form of the given function.

Expert Solution

Answer to Problem 13E

The differentiate form of the given function is f'(x)=excscx(1+xxcotx) .

Explanation of Solution

Given:

The given functionis f(x)=xexcscx .

Calculation:

Use product rule of three function.

  (fgh)'=ghf'+fhg'+fgh'

Use derivative rule.

  ddx(xn)=nxn1,ddx(ex)=ex and ddx(cscx)=cscxcotx

  f(x)=xexcscxddxf(x)=excscxddx(x)+xcscxddx(ex)+xexddx(cscx)f'(x)=excscx+xcscxex+xex(cscxcotx)f'(x)=excscx+xexcscxxexcscxcotxf'(x)=excscx(1+xxcotx)

Hence the differentiate form of the given functionis f'(x)=excscx(1+xxcotx) .

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