# Find the differentiate form of the given equation.

### Single Variable Calculus: Concepts...

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

### 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

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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