Question

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

Answer 1

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`