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Popular Calculus >

derivative of-e^{-x}x^2+e^{-x}x

Solution

\frac{d}{d x} (- e^{- x} x^{2} + e^{- x} x)

Solution

e^{- x} x^{2} - 3 e^{- x} x + e^{- x}

Solution steps

\frac{d}{d x} (- e^{- x} x^{2} + e^{- x} x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (e^{- x} x) = - e^{- x} x + e^{- x}

= - (- e^{- x} x^{2} + 2 e^{- x} x) - e^{- x} x + e^{- x}

Simplify

= e^{- x} x^{2} - 3 e^{- x} x + e^{- x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of-e^{-x}x^2+e^{-x}x ?
The derivative of-e^{-x}x^2+e^{-x}x is e^{-x}x^2-3e^{-x}x+e^{-x}
What is the first derivative of-e^{-x}x^2+e^{-x}x ?
The first derivative of-e^{-x}x^2+e^{-x}x is e^{-x}x^2-3e^{-x}x+e^{-x}