Question

What is the derivative of `g(x)= x^2*sqrt(1-x^2)`?

Answer 1

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

For the product rule:

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

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

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