Question

What is the derivative of `ln(1-x^2)^(1/2)`?

Answer 1

I found: `f'(x)=-x/(1-x^2)`

Explanation:

I would write it as:
`f(x)=ln[(1-x^2)^(1/2)]=1/2ln(1-x^2)` using one of the properties of logs.
Then derive using the Chain Rule for the log and its argument as:
`f'(x)=1/2*1/(1-x^2)*(-2x)=-x/(1-x^2)`