Quotient rule with exponential and power function

Identify the numerator and denominator: let $u = e^x$ so $u' = e^x$, and let $v = x^2$ so $v' = 2x$. Apply the quotient rule formula $\dfrac{u'v - uv'}{v^2}$ to get $f'(x) = \dfrac{e^x \cdot x^2 - e^x \cdot 2x}{(x^2)^2}$.

Simplify the numerator by factoring out $e^x \cdot x$: the numerator becomes $e^x x (x - 2)$, and the denominator is $x^4$. Canceling one factor of $x$ gives $f'(x) = \dfrac{e^x(x-2)}{x^3}$.

The common factor canceled from both numerator and denominator was x. In the numerator e^x·x·(x-2), one factor of x was canceled with one factor of x from the denominator x⁴, leaving e^x(x-2) in the numerator and x³ in the denominator.