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 28E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 28E

The derivative of the given function is dydx=ektanx[k2xsec2x] .

Explanation of Solution

Given:

The given function is y=ektanx .

Calculation:

  y=ektanx

Apply chain rule.

  df(a)dx=dfdadadx

Let f=ea,a=ktanx

  dydx=dda(ea)ddx(ktanx)

Use derivative rule.

  ddx(ex)=ex,ddx(xn)=nxn1andddx(tanx)=sec2x .

  dydx=(ea)(ksec2x12x)dydx=ea[k2xsec2x]

Substitute the value of a=ktanx .

  dydx=ektanx[k2xsec2x]

Hence the derivativeof the given function is dydx=ektanx[k2xsec2x] .

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