Question

Find the derivative of
y=ln((1+e^x)/(1-e^x))

I know that the derivative of y=ln(1+e^x) would be (e^x)/(1+e^x), but I'm not sure what to do with the 1-e^x on the bottom here. Can someone help please? Thanks!

Answer 1

In google type:
wolfram alpha

When you see lis of results click on:

Wolfram Alpha:Computational Knowledge Engine

When page be open in rectangle type:

derivartive ln((1+e^x)/(1-e^x))

and click option =

After few secons you will see result.

Then clic option Show steps

Answer 2

first of all recall that
ln (A/B) = ln A - ln B
so
y = ln((1+e^x)/(1-e^x) )
= ln (1+e^x) - ln (1-e^x)
dy/dx = e^x/(1+e^x) - (-e^x)/(1 - e^x)

simplify as needed

Answer 3

Okay, thanks guys!