`g(x) = ln(xsqrt(x^2 - 1))` Differentiate the function.

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Chapter 3, 3.6 - Problem 11 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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mathace | (Level 3) Assistant Educator

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Given: `g(x)=ln(xsqrt(x^2-1))`

Rewrite the equation using the Law of exponents. Then find the derivative.

`g(x)=lnx+(1)/(2)ln(x^2-1)`

`g'(x)=(1)/(x)+(1)/(2(x^2-1))(2x)`

The derivative is:

`g'(x)=(1)/(x)+(x)/(x^2-1)`

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