Question

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

Answer 1

`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