Question

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

Answer 1

It is `f'(x)=(2x)/((sqrt(x^2-1))*(x^2+1)^(3/2))`

Explanation:

We have that

`f(x)=sqrt((x^2-1)/(x^2+1))` hence

`f'(x)=1/2*1/(sqrt((x^2-1)/(x^2+1)))*((x^2-1)/(x^2+1))'`

`f'(x)=1/2*sqrt(x^2+1)/sqrt(x^2-1)*((2x(x^2+1)-(x^2-1)2x)/(x^2+1))`

`f'(x)=1/2*sqrt(x^2+1)/sqrt(x^2-1)*(4x/(x^2+1)^2)`

`f'(x)=(2x)/((sqrt(x^2-1))*(x^2+1)^(3/2))`