Help with derivatives of natural logs

[musiciskey]

Homework Statement

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

Homework Equations

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+e^x))⁶] = 6(ln(1 + e^x)⁵* d/dx(ln(1 + e^x))

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+e^x))⁶ and ln(1+e^x)⁶ = ln[(1+e^x)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+e^x))⁶ and ln(1+e^x)⁶ = ln[(1+e^x)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 + e^x)⁶, as you seem to think.
Because the log expression is raised to the 6th power, the derivative is 6( ln(1 + e^x))⁵ * d/dx(ln(1 + e^x)).