Chapter 3 - Section 3.6 - Derivatives of Logarithmic Functions - 3.6 Exercises - Page 223: 12

$h'(x)=\frac{1}{\sqrt{x^2-1}}$

$h(x)=\ln(x+\sqrt{x^2-1})\\ h'(x)=\frac{1}{x+\sqrt{x^2-1}}\times{(1+\frac{x}{\sqrt{x^2-1}})}\\ h'(x)=\frac{1}{x+\sqrt{x^2-1}}\times{\frac{\sqrt{x^2-1}+x}{\sqrt{x^2-1}}}\\ h'(x)=\frac{1}{\sqrt{x^2-1}}$