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

1 Answer

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))