# How do you find the derivative of g(x) = sqrt(x^2-1)?

Mar 21, 2016

$\frac{\mathrm{dg}}{\mathrm{dx}} = \frac{x}{\sqrt{{x}^{2} - 1}}$

#### Explanation:

We have to use here the concept of function of a function which uses the formula for chain rule.

As g(x)=sqrt(h(x) where $h \left(x\right) = {x}^{2} - 1$ and according to chain rule

$\frac{\mathrm{dg}}{\mathrm{dx}} = \frac{\mathrm{dg}}{\mathrm{dx}} \times \frac{\mathrm{dh}}{\mathrm{dx}}$

Hence $\frac{\mathrm{dg}}{\mathrm{dx}} = \frac{1}{2 \sqrt{{x}^{2} - 1}} \times 2 x$

or $\frac{\mathrm{dg}}{\mathrm{dx}} = \frac{x}{\sqrt{{x}^{2} - 1}}$