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

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

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

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

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Popular >

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

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

Solution steps

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

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

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

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

Simplify

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

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

e^{- 0.75 t} \cdot cos (4 t)

\frac{d}{d x} (3^{(1 - 3 x)})

20 + \frac{10}{s} \cdot \frac{1}{8 s + 1}

\int \frac{1}{y ^{2} y ^{2} - 7} d y

\frac{sin ( 2 x ) cos ( 3 x )}{x}

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