# 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 12E
To determine

## Find the differentiate form of the given equation.

Expert Solution

The differentiate form of the given equationis zx dydx=csc2x+cscxcotx .

### Explanation of Solution

Given:

The given equationis y=1secxtanx .

Calculation:

Rewrite the given function.

y=1secxtanxy=1tanxsecxtanxy=cotx1cosxcosxsinxy=cotxcscx

Use the rule ddx(cotx)=csc2x and ddx(cscx)=cscxcotx

dydx=csc2x(cscxcotx)dydx=csc2x+cscxcotx

Hence the differentiate form of the given equationis dydx=csc2x+cscxcotx .

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