`y = xsqrt(1 - x^2)` Find the derivative of the function.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to use the product and chain rules to evaluate the derivative of the function, such that:

`f'(x) = (x)'(sqrt(1 - x^2)) + (x)(sqrt(1 - x^2))'`

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

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

Hence, evaluating the derivative of the function, using the product rule, yields` f'(x) = (sqrt(1 - x^2)) - (x^2)/(sqrt(1 - x^2))).`