# Find the derivative of the given function.

### 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 3.4, Problem 33E
To determine

## Find the derivative of the given function.

Expert Solution

The derivative of the given function is dydx=2cot(sinx)csc2(sinx)cosx .

### Explanation of Solution

Given:

The given function is y=cot2(sinθ) .

Calculation:

y=cot2(sinθ)

Apply chain rule.

Let f=a2,a=cot(sinx)

dydx=dda(a2)ddx(cot(sinx))

Use derivative rule.

ddx(xn)=nxn1 .

Substitute the value of a=cot(sinx) .

dydx=2cot(sinx)ddx(cot(sinx))

Apply chain rule.

Let f=cot(a),a=sinx

dydx=2cot(sinx)dda(cota)ddx(sinx)

Use derivative rule.

ddx(cotx)=csc2xandddx(sinx)=cosx .

dydx=2cot(sinx)csc2acosx

Substitute the value of a=sinx .

dydx=2cot(sinx)csc2(sinx)cosxdydx=2cot(sinx)csc2(sinx)cosx

Hence the derivativeof the given function is dydx=2cot(sinx)csc2(sinx)cosx .

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