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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

derivative of y=e^pi derivative of

y = e^{π}

limit as x approaches pi/2 of (sin(x)-cos(x))^{tan(x)}

x \to \frac{π}{2} lim ((sin (x) - cos (x))^{t a n (x)})

integral of 8xe^{9x}

\int 8 x e^{9 x} d x

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x, 8

limit as x approaches 0 of ((484+x)^{0.5}-22)/x

x \to 0 lim (\frac{( 484 + x ) ^{0.5} - 22}{x})

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)