`g(x) = sqrt(x^2 - 1) sec^-1(x)` Find the derivative of the function. Simplify where possible.

Textbook Question

Chapter 3, 3.5 - Problem 52 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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embizze | High School Teacher | (Level 1) Educator Emeritus

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Find `g'(x) ` if `g(x)=sqrt(x^2-1)sec^(-1)(x) ` :

Use the product rule:

`g'(x)=sqrt(x^2-1)*1/(|x|sqrt(x^2-1))+(1/2)(x^2-1)^(-1/2)(2x)sec^(-1)(x) `

`=1/|x|+(xsec^(-1)(x))/sqrt(x^2-1) ` or

`=1/sqrt(x^2)+(xsec^(-1)(x))/sqrt(x^2-1) `

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