How do you find the derivative of g(x) = sqrt(x^2-1)g(x)=x21?

1 Answer
Mar 21, 2016

(dg)/(dx)=x/sqrt(x^2-1)dgdx=xx21

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)g(x)=h(x) where h(x)=x^2-1h(x)=x21 and according to chain rule

(dg)/(dx)=(dg)/dxxx(dh)/(dx)dgdx=dgdx×dhdx

Hence (dg)/(dx)=1/(2sqrt(x^2-1))xx2xdgdx=12x21×2x

or (dg)/(dx)=x/sqrt(x^2-1)dgdx=xx21