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Popular >

derivative of xe^{-10x}

Solution

\frac{d}{d x} (x e^{- 10 x})

Solution

e^{- 10 x} - 10 e^{- 10 x} x

Solution steps

\frac{d}{d x} (x e^{- 10 x})

Apply the Product Rule:

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

f = x, g = e^{- 10 x}

= \frac{d x}{d x} e^{- 10 x} + \frac{d}{d x} (e^{- 10 x}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{- 10 x}) = - 10 e^{- 10 x}

= 1 \cdot e^{- 10 x} + (- 10 e^{- 10 x}) x

Simplify

= e^{- 10 x} - 10 e^{- 10 x} x

Graph

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x \to 0 + lim (x + ln (x))

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n = 1 \sum \infty \frac{n}{9 n ^{2} + 1}

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\int \frac{x ^{2} - 100}{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of xe^{-10x} ?
The derivative of xe^{-10x} is e^{-10x}-10e^{-10x}x
What is the first derivative of xe^{-10x} ?
The first derivative of xe^{-10x} is e^{-10x}-10e^{-10x}x