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

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Answer 1 · 2016-01-14T21:38:11

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

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

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

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

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