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Popular >

derivative of axe^{-2x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= a \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}

= a (\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}

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

Simplify

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

Popular Examples

(dy)/(dx)=(x+1)/(e^{3y+9)}

\frac{d y}{d x} = \frac{x + 1}{e ^{3 y + 9}}

limit as x approaches 2 of (10-3x)^2

x \to 2 lim ((10 - 3 x)^{2})

integral from 1 to 36 of e^{sqrt(x)}

\int_{1}^{36} e^{x} d x

area y= 9/(sqrt(9x-x^2)),x=1,x=7.5 area

y = \frac{9}{9 x - x ^{2}}, x = 1, x = 7.5

integral from-1 to 1 of 2-x^2

\int_{- 1}^{1} 2 - x^{2} d x

Frequently Asked Questions (FAQ)

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