How do you find the derivative of sqrt(1-x^2)?

1 Answer
Oct 8, 2016

(dy)/(dx)=-x(1-x^2)^(-1/2)

Explanation:

Use chain rule:
(dy)/(dx)=(dy)/(du)x(du)/(dx)

Let u=1-x^2,
then (du)/(dx)=-2x and dy/(du)=1/2(1-x^2)^(-1/2)

Plugging it into the chain rule,
(dy)/(dx)=-2x x 1/2(1-x^2)^(-1/2)=-x(1-x^2)^(-1/2)