Question

y(x) = ln[sqrt(2 − x^2)]
what is y'(x)?

Answer 1

\[f(x)=\ln(g(x))\]
\[f'(x)=\frac{g'(x)}{g(x)}\]

Answer 2

thanks, that's useful to know!! is that rule called anything in particular?

Answer 3

oh i have a better idea, i wasn't paying attention

Answer 4

\[f(x)=\ln(\sqrt{2-x^2})\]
\[f(x)=\frac{1}{2}\ln(2-x^2)\]take the derivative now

Answer 5

it is the chain rule for logs and it is very useful

Answer 6

it is always the case that
\[\frac{d}{dx}\ln(g(x))=\frac{g'(x)}{g(x)}\]

Answer 7

Can you follow the instruction?