Question

How do you differentiate `f(x)=x / (1-x^2)^(1/2)` using the quotient rule?

Answer 1

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

Explanation:

`f'(x)=(sqrt(1-x^2)-x*1/2*(1-x^2)^(-1/2)*(-2x))/(1-x^2)`
so we get

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