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Popular >

derivative of axe^{-x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= a \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}

= a (\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}

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

Simplify

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

Popular Examples

(\partial)/(\partial x)(ln(ax+by))

\frac{\partial}{\partial x} (ln (a x + b y))

sum from n=1 to infinity of (1)^n

n = 1 \sum \infty (1)^{n}

integral of (x^2+1)^2

\int (x^{2} + 1)^{2} d x

integral of (4x^2+7x+4)/((x^2+1)^2)

\int \frac{4 x ^{2} + 7 x + 4}{( x ^{2} + 1 ) ^{2}} d x

derivative of (x^3-5x^2/(x^8-4))

\frac{d}{d x} (\frac{x ^{3} - 5 x ^{2}}{x ^{8} - 4})

Frequently Asked Questions (FAQ)

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