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Popular >

derivative of xe^{-sqrt(x)}

Solution

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

Solution

e^{- x} - \frac{e ^{- x} x}{2}

Solution steps

\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}

= \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}) = - \frac{e ^{- x}}{2 x}

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

Simplify

1 \cdot e^{- x} + (- \frac{e ^{- x}}{2 x}) x : e^{- x} - \frac{e ^{- x} x}{2}

= e^{- x} - \frac{e ^{- x} x}{2}

Popular Examples

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tangent of f(x)=2sqrt(x),\at x=4 tangent of

f (x) = 2 x, at x = 4

y^'=(3x^2+2x-4)/(2y-4),y(2)=0

y^{^{'}} = \frac{3 x ^{2} + 2 x - 4}{2 y - 4}, y (2) = 0

inverse oflaplace (2s)/((s^2+1)^2(s+1))inverse laplace

\frac{2 s}{( s ^{2} + 1 ) ^{2} ( s + 1 )}

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\frac{d}{d x} (\frac{x cos ( x ) - sin ( x )}{x ^{2}})

Frequently Asked Questions (FAQ)

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