   Chapter 8.4, Problem 20E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Differentiating Trigonometric Functions In Exercises 1-28, find the derivative of the trigonometric function. See Examples 1, 2, 3, y = e − 2 x 2 cot x

To determine

To calculate: The derivative of the trigonometric function y=e2x2cotx.

Explanation

Given Information:

The provided trigonometric function is y=e2x2cotx.

Formula used:

Cotangent differentiation rule:

ddx[cotu]=csc2ududx

Product rule of differentiation:

ddx[a(x)b(x)]=a(x)b(x)+b(x)a(x)

Exponential rule of differentiation:

ddx[eu]=eududx

General power rule of differentiation:

ddx[xn]=nxn1

Calculation:

Consider the provided trigonometric function is,

y=e2x2cotx

Apply the product rule of differentiation to find the derivative of the above function.

dydx=e2x2ddx[cotx]+cotxddx[e2x2]

Differentiate the above function using general power rule, cotangent and exponential differentiation rule

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