How do you find the derivative of $f (x) = x^{2} e^{- x}$ $f(x)=x^2e^-x$ ?

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How do you find the derivative of $f (x) = x^{2} e^{- x}$ $f(x)=x^2e^-x$ ?

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Answer 1 · 2017-02-25T11:46:22

$f'(x)=2xe^-x-x^2e^-x$

Explanation:

differentiate using the $color(blue)"product rule"$

$"Given "f(x)=g(x).h(x)" then"$

$color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=g(x)h'(x)+h(x)g'(x))color(white)(2/2)|)))$

$"here "g(x)=x^2rArrg'(x)=2x$

$"and "h(x)=e^-xrArrh'(x)=e^-x.d/dx(-x)=-e^-x$

$rArrf'(x)=x^2(-e^-x)+e^-x(2x)$

$color(white)(rArrf'(x))=2xe^-x-x^2e^-x$

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How do you find the derivative of $f (x) = x^{2} e^{- x}$ $f(x)=x^2e^-x$ ?

1 Answer

Explanation:

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How do you find the derivative of $f (x) = x^{2} e^{- x}$ $f(x)=x^2e^-x$ ?