# 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 7E
To determine

## Find the differentiate form of the given equation.

Expert Solution

The differentiate form of the given equationis dydt=sint(2tc)+t2cost .

### Explanation of Solution

Given:

The given equationis y=ccost+t2sint .

Calculation:

Use product rule.

(fg)'=fg'+gf'

dydt=cddt(cost)+t2ddt(sint)+sintddt(t2)

Use the derivative rule

ddx(cosx)=sinx,ddx(sinx)=cosx and ddx(xn)=nxn1 .

dydt=cddt(cost)+t2ddt(sint)+sintddt(t2)dydt=csint+t2cost+2tsintdydt=sint(2tc)+t2cost

Hence the differentiate form of the given equationis dydt=sint(2tc)+t2cost .

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