What is the second derivative of $f(x)=e^x/x^2$ ?

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Answer 1 · 2016-05-26T03:39:17

Using the quotient rule we get

$f'(x)=[e^x*(x-2)]/x^2$

Using the quotient rule again for the above we get

$f''(x)=[e^x*(x^2-4x+6)]/x^4$

Footnote

The quotient rule for a function such as $f(x)=(p(x))/(q(x))$ is

$f'(x)=[p'(x)*q(x)-p(x)*q'(x)]/[q(x)]^2$

where $f'(x)=df(x)/dx$

What is the second derivative of f(x)=e^x/x^2 f(x)=e^x/x^2 ?