What is the derivative of (-xe^{-x}+e^{-x}/(e^x)) ?

The derivative of (-xe^{-x}+e^{-x}/(e^x)) is (2x-3)/(e^{2x)}

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

The first derivative of (-xe^{-x}+e^{-x}/(e^x)) is (2x-3)/(e^{2x)}

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Popular >

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

\frac{2 x - 3}{e ^{2 x}}

Solution steps

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

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

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

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

Simplify

\frac{( e ^{- x} x - 2 e ^{- x} ) e ^{x} - e ^{x} ( - x e ^{- x} + e ^{- x} )}{( e ^{x} ) ^{2}} : \frac{2 x - 3}{e ^{2 x}}

= \frac{2 x - 3}{e ^{2 x}}

n = 0 \sum \infty \frac{n + 1}{e ^{n}}

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

3 6 x^{4} + 7 x^{3}

\frac{d}{d x} ((6 x + 4) (3 x^{2} + 2))

x \to - \infty lim (\frac{5 x ^{4} + e ^{5 x}}{x ^{4}})

What is the derivative of (-xe^{-x}+e^{-x}/(e^x)) ?
The derivative of (-xe^{-x}+e^{-x}/(e^x)) is (2x-3)/(e^{2x)}
What is the first derivative of (-xe^{-x}+e^{-x}/(e^x)) ?
The first derivative of (-xe^{-x}+e^{-x}/(e^x)) is (2x-3)/(e^{2x)}