Question

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

Answer 1

`(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)`