Question

Find the derivative.

f(x)=ln(8-e^-x)

I got -e^-x/8-e^-x
but it was wrong.
WHAT DID I DOOOO?!

Answer 1

You're close, but missing something.

You understand that the derivative of ln(x) is 1/x, so
you have (8-e^(-x)) in the denominator, which is the first step correctly done.

The next step is to apply the chain rule to derive the argument of log,namely
d(8-e^(-x))/dx
=(0-(-e^(-x)))
=<b>+</b>e^(-x))

So the final answer should be
<b>+</b>e^(-x))/(8-e^-x)

Another source of error is that you do not appear to use parentheses appropriately.
Even if you had given the answer as
e^-x/8-e^-x
it would be incorrect, because it means
e^-(x/8)-e^-x
properly written (especially for a computer answer), it should be:
(e^-x)/(8-e^-x)
or even
(e^(-x))/(8-e^(-x))