Question

f (x)=x^2 /e^x then f'(1) is equal to
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Answer 1

Step-by-step explanation:

We have,

$f(x) = y = \frac{ {x}^{2} }{ {e}^{x} }$

$\frac{dy}{dx} = \frac{2x( {e}^{x} ) - {x}^{2} ( {e}^{x} )}{ {e}^{2x} }$

$= \frac{(2x - {x}^{2} )}{ {e}^{x} }$

Now,

$( \frac{dy}{dx}) _{x = 1} = \frac{1}{e} = {e}^{ - 1}$