How do I find the derivative of #F(y) = yln(9 + e^y)#?

1 Answer
May 7, 2018

#f'(y)=ye^y/(9+e^y)+ln(9+e^y)#

Explanation:

First, turn it into #f(x)=xln(9+e^x)#
(It is not necessary but x is less confusing in the equation)
Next, apply product rule
#f'(x)=x*(1/(9+e^x) * e^x)+1*(ln(9+e^x))#
Note the chain rule used when taking derivative of #ln(9+e^x)#
Simplify
#f'(x)=xe^x/(9+e^x)+ln(9+e^x)#
Lastly, replace all x with y