Question

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

Answer 1

`(dg)/(dx)=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(x)=x^2-1` and according to chain rule

`(dg)/(dx)=(dg)/dxxx(dh)/(dx)`

Hence `(dg)/(dx)=1/(2sqrt(x^2-1))xx2x`

or `(dg)/(dx)=x/sqrt(x^2-1)`