   Chapter 8.4, Problem 16E ### 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  =  ( x   +   3 )  csc  x

To determine

To calculate: The derivative of the trigonometric function y=(x+3)cscx.

Explanation

Given Information:

The provided trigonometric function is y=(x+3)cscx.

Formula used:

Cosecant differentiation rule:

ddx[cscu]=cscucotududx

Product rule of differentiation:

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

General power rule of differentiation:

ddx[xn]=nxn1

Calculation:

Consider the provided trigonometric function is,

y=(x+3)cscx

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

dydx=(x+3)ddx[cscx]+cscxddx[x+3]

Differentiate the above function using general power rule and cosecant differentiation rule

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