Question

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

Answer 1

The answer is: `x/sqrt((1-x^2)^3)`.

This is because the function can be written:

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

So:

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

`=x/sqrt((1-x^2)^3)`.