help with derivatives of natural logs

[musiciskey]

1. The problem statement, all variables and given/known data

(ln(1+e^x))^6

2. Relevant equations



3. The attempt at a solution
Honestly I haven't done this in 3 years and a friend asked me to help them with it. I'm at a bit of loss.

[Mark44]

I'll help you with one of the steps.
d/dx[ (ln(1+ex))6] = 6(ln(1 + ex)5* d/dx(ln(1 + ex))

Is that enough of a start?

[musiciskey]

I'll pass it on to her and find out. Thanks.

[Bohrok]

There's a difference between (ln(1+ex))6 and ln(1+ex)6 = ln[(1+ex)6]
The ln has the exponent, not the argument of the ln, so you can't pull the exponent out in front.

[Mark44]

There's a difference between (ln(1+ex))6 and ln(1+ex)6 = ln[(1+ex)6]
The ln has the exponent, not the argument of the ln, so you can't pull the exponent out in front.
I understand that there is a difference.

The problem as posted is
(ln(1+e^x))^6

As you can see, it was NOT ln(1 + ex)6, as you seem to think.
Because the log expression is raised to the 6th power, the derivative is 6( ln(1 + ex))5 * d/dx(ln(1 + ex)).