Question

What is the derivative of f(x)= ln(e^-x^2)

Answer 1

\[f(x)=\ln(e^{-x^{2}})\]

Answer 2

You have to use the chain rule.
first the derivative of ln(g(x)) = (1/g(x))*g'(x) right?

Answer 3

say g(x) = exp(-x^2)

Answer 4

now what is the derivative of e^h(x)? it is e^h(x) * h'(x)

Answer 5

say h(x) = -x^2

Answer 6

what is the derivative of h(x)=-x^2? it will be -2x

Answer 7

now plug it all in

Answer 8

derivative of ln(e^(-x^2)) = (1/(e^(-x^2)))*(e^(-x^2))*(-2x)

Answer 9

oh ok so first the derivative of ln(x)= 1/x so that's why 1/e^-x^2 right ...

Answer 10

and then I know that the derivative of e^x is simply e^x unless it's e^(fx) then it is e^(fx) * f'(x)

Answer 11

I'm getting it now lol ^_^ thanks

Answer 12

that's right!

Answer 13

you have to split all these functions and recognize their derivatives

Answer 14

then you just "chain" it all together

Answer 15

;)