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 14E
To determine

Find the differentiate form of the given equation.

Expert Solution

Answer to Problem 14E

The differentiate form of the given equation is dydx=xtanx(2sinx+xcosx+xsecx) .

Explanation of Solution

Given:

The given equationis y=x2sinxtanx .

Calculation:

Use product rule of three function.

  (fgh)'=ghf'+fhg'+fgh'

Use derivative rule.

  ddx(xn)=nxn1,ddx(sinx)=cosx and ddx(tanx)=sec2x

  y=x2sinxtanxdydx=sinxtanxddx(x2)+x2tanxddx(sinx)+x2sinxddx(tanx)dydx=sinxtanx2x+x2tanxcosx+x2sinxsec2xdydx=sinxtanx2x+x2tanxcosx+x2tanxsecxdydx=xtanx(2sinx+xcosx+xsecx)

Hence the differentiate form of the given equationis dydx=xtanx(2sinx+xcosx+xsecx) .

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