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Popular Calculus >

derivative of-2xe^{-x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= - 2 \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}

= - 2 (\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}

= - 2 (1 \cdot e^{- x} + (- e^{- x}) x)

Simplify

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

Graph

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Frequently Asked Questions (FAQ)

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