How do you differentiate # f(x)=ln (e^x/(e^x+1))#?

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Answer 1 · 2017-05-08T13:35:16

#f'(x) = 1/(e^x + 1)#

This can be rewritten as

#f(x) = ln(e^x) - ln(e^x + 1)#

#f(x) = xlne - ln(e^x + 1)#

We know that #ln(e) = 1#.

#f(x) = x - ln(e^x + 1)#

Now use the chain and power rule to differentiate.

#f'(x) = 1 - (e^x)/(e^x+ 1)#

#f'(x) = (e^x + 1 - e^x)/(e^x + 1)#

#f'(x) = 1/(e^x + 1)#

Hopefully this helps!