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Popular >

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

Solution

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

Solution

2 e^{- 2 x} x - 2 e^{- 2 x} x^{2}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = e^{- 2 x}

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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