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Popular >

derivative of 2xe^{-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

Popular Examples

sum from n=5 to infinity of (5^n)/(6^n)

n = 5 \sum \infty \frac{5 ^{n}}{6 ^{n}}

derivative of 5/(4x^3+4)

\frac{d}{d x} (\frac{5}{4 x ^{3} + 4})

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\int 28 (7 x - 2)^{- 5} d x

(\partial)/(\partial x)(((2x-2y))/(4x+2y))

\frac{\partial}{\partial x} (\frac{( 2 x - 2 y )}{4 x + 2 y})

(\partial)/(\partial x)(t^2e^{(x^2)/(2t)})

\frac{\partial}{\partial x} (t^{2} e^{\frac{x ^{2}}{2 t}})

Frequently Asked Questions (FAQ)

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