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Popular >

derivative of (sqrt(x)/(e^x))

Solution

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

Solution

\frac{1 - 2 x}{2 e ^{x} x}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

= \frac{1 - 2 x}{2 e ^{x} x}

Popular Examples

y^{^{'}} + 2 y = 6 e^{x}

(dy)/(dx)=xe^{-y}+10e^{-y}

\frac{d y}{d x} = x e^{- y} + 10 e^{- y}

integral of (14x)/(sqrt(1-x^4))

\int \frac{14 x}{1 - x ^{4}} d x

(\partial)/(\partial x)(xy)

\frac{\partial}{\partial x} (x y)

(\partial)/(\partial t)(10e^{-0.25x}sin((2pi)/(365)t-0.25x))

\frac{\partial}{\partial t} (10 e^{- 0.25 x} sin (\frac{2 π}{365} t - 0.25 x))

Frequently Asked Questions (FAQ)

What is the derivative of (sqrt(x)/(e^x)) ?
The derivative of (sqrt(x)/(e^x)) is (1-2x)/(2e^xsqrt(x))
What is the first derivative of (sqrt(x)/(e^x)) ?
The first derivative of (sqrt(x)/(e^x)) is (1-2x)/(2e^xsqrt(x))