What is the second derivative of $f(x)= ln (x^3+e^x)$ ?

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Answer 1 · 2016-02-04T21:59:14

$f''(x)=((x^3+e^x)(6x+e^x)-(3x^2+e^x)^2)/(x^3+e^x)^2$

We first use the log rule to find

$f'(x)=(3x^2+e^x)/(x^3+e^x)$

We now use the quotient rule to find

$f''(x)=((x^3+e^x)(6x+e^x)-(3x^2+e^x)(3x^2+e^x))/(x^3+e^x)^2$

What is the second derivative of f(x)= ln (x^3+e^x)f(x)= ln (x^3+e^x)?