Question

How do you find the derivative of `(1-y^2)^(1/2)`?

Answer 1

`-y/sqrt(1-y^2)`

Explanation:

Use the power rule and chain rule: `(u^n)' = n u^(n-1) u'`

`n = 1/2` so `n-1 = -1/2`; `u = 1-y^2`, so `u' = -2y`

Using substitution, the derivative is:

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