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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find the derivative of the function. Simplify where possible.

51. y = sin–1(2x + 1)

To determine

To find: The derivative of the function.

Explanation

Given:

The function is y=sin1(2x+1).

Derivative rules:

(1) Chain rule: If y=f(u) and u=g(x)  are both differentiable function, then

dydx=dydududx.

(2) Derivative of the inverse trigonometric function: ddx(sin1(x))=11x2.

Calculation:

Obtain the derivative of the function.

Consider the function y=sin1(2x+1)

Differentiate the function with respect to x,

dydx=ddx(sin1(2x+1))

Let u=2x+1.

dydx=ddx(sin1(u))

Apply the chain rule (1),

dydx=ddu(sin1(u))dudx=(11u2)d

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