Question

What is the second derivative of `f(x)= ln (x+e^x)`?

Answer 1

`f''(x)=((x-2)e^x-1)/(x+e^x)^2`

Explanation:

From the standard rules of differentiating log functions we get

`f'(x)=1/(x+e^x)*(1+e^x)`

From the quotient rule we now get

`f''(x)=((x+e^x) * e^x-(1+e^x) * (1+e^x))/(x+e^x)^2`

`=((x-2)e^x-1)/(x+e^x)^2`.