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Popular >

derivative of 2xe^{-x}

Solution

derivative of

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)

Popular Examples

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\frac{1}{( s ^{2} + 9 ) ^{2}}

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\frac{\partial}{\partial y} (4 y sin (x^{2} y))

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)