derivative of: f(x)= e^x/x^2

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use the quotient rule to evaluate the derivative of the rational function, such that:

`f'(x) = ((e^x)'*x^2 - e^x*(x^2)')/(x^4)`

`f'(x) = (e^x*x^2 - 2x*e^x)/(x^4)`

Factoring out `x*e^x` yields:

`f'(x) = (x*e^x(x - 2))/(x^4)`

Reducing duplicate factors yields:

`f'(x) = (e^x(x - 2))/(x^3)`

Hence, evaluating the derivative of the given function, yields `f'(x) = (e^x(x - 2))/(x^3).`