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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Find the derivative. Simplify where possible.

45. y = coth–1(sec x)

To determine

To find: The derivative of the function.

Explanation

Given:

The function y=coth1(secx).

Derivative rules:

(1) The chain rule: dydx=dydududx

(2) The derivative of the inverse hyperbolic cot function ddx(coth1x)=11x2.

Calculation:

The derivative of the function y=coth1(secx) is computed as follows,

dydx=ddx(coth1(secx))

Let u=secx and apply the chain rule,

dydx=ddx(coth1u)=ddu(coth1u)ddx(u)=11u2(dudx</

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