Question

Differentiate the function g(x) = ln[x(sqrt(x^2 - 1))]

Answer 1

g(x) = ln[x(sqrt(x^2 - 1))]
g'(x) = 1/[x(sqrt(x^2 - 1))] * (x^2/sqrt(x^2 - 1) + sqrt(x^2 - 1)) = ((x^2 + x^2 - 1)/sqrt(x^2 - 1)) / x(sqrt(x^2 - 1)) = (2x^2 - 1) / x(x^2 - 1) = (2x^2 - 1) / (x^3 - x)