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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Graph

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\int_{0}^{4} x^{2} 16 - x^{2} d x

Frequently Asked Questions (FAQ)

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