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

1 Answer
Mar 21, 2016

Answer:

#(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)#