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Popular >

derivative of 7xe^{-x}

Solution

\frac{d}{d x} (7 x e^{- x})

Solution

7 (e^{- x} - e^{- x} x)

Solution steps

\frac{d}{d x} (7 x e^{- x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (x e^{- x})

Apply the Product Rule:

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

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

= 7 (\frac{d x}{d x} e^{- x} + \frac{d}{d x} (e^{- x}) x)

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

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

= 7 (1 \cdot e^{- x} + (- e^{- x}) x)

Simplify

= 7 (e^{- x} - e^{- x} x)

Popular Examples

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x \to 0 lim (\frac{1}{e ^{2 x} - 1})

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\int x cos (5 x^{2}) d x

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x \to 2 lim (\frac{4 x}{x - 4})

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

Frequently Asked Questions (FAQ)

What is the derivative of 7xe^{-x} ?
The derivative of 7xe^{-x} is 7(e^{-x}-e^{-x}x)
What is the first derivative of 7xe^{-x} ?
The first derivative of 7xe^{-x} is 7(e^{-x}-e^{-x}x)