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Popular >

derivative of cxe^{-2x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= c \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}

= c (\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}

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

Simplify

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

Popular Examples

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\frac{d}{d x} (\frac{2 sin ( x )}{x})

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x \to 2 lim (\frac{x ^{2} - 4}{x ^{2} - 3 - 1})

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\frac{\partial}{\partial z} (y z^{2})

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\frac{\partial}{\partial x} (ln (x \cdot y))

taylor X^{9/6},8,5 taylor

X^{\frac{9}{6}}, 8, 5

Frequently Asked Questions (FAQ)

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