Question

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

Answer 1

the answer `y'=[2x-4x^3]/[2sqrt[x^2-x^4]]`

Explanation:

`y= (x) / ((1- x^2) ^ (-1/2))`

we can rewrite it

`y=x*(1-x^2)^(1/2)=x*sqrt(1-x^2)`

`y=sqrt[x^2(1-x^2)]=sqrt[x^2-x^4]`

now derivate it

`y'=[2x-4x^3]/[2sqrt[x^2-x^4]]`