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Popular >

derivative of sqrt(x)*e^{-x}

Solution

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

Solution

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

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

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

Popular Examples

(dy)/(dx)=9xe^y,y(0)=0

\frac{d y}{d x} = 9 x e^{y}, y (0) = 0

tangent of f(x)=2x^2-1,\at x=-1 tangent of

f (x) = 2 x^{2} - 1, at x = - 1

(dy)/(dx)=x^2y-y+x^2-1

\frac{d y}{d x} = x^{2} y - y + x^{2} - 1

integral of 3x^4

\int 3 x^{4} d x

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

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

Frequently Asked Questions (FAQ)

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