What is the derivative of (e^{-x}/(x+1)) ?

The derivative of (e^{-x}/(x+1)) is (-e^{-x}x-2e^{-x})/((x+1)^2)

What is the first derivative of (e^{-x}/(x+1)) ?

The first derivative of (e^{-x}/(x+1)) is (-e^{-x}x-2e^{-x})/((x+1)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{0.3 ( 5 ^{x} )}{x ^{3}})

\frac{d}{d x} ((2 x - 21) (x^{2} + 36))

\frac{d}{d x} (x \cdot (x^{2} + 1)^{\frac{1}{2}})

x \to \infty lim (\frac{5 x}{7 x - 4 x ^{3}})

n = 1 \sum \infty \frac{n}{n ^{2}}

What is the derivative of (e^{-x}/(x+1)) ?
The derivative of (e^{-x}/(x+1)) is (-e^{-x}x-2e^{-x})/((x+1)^2)
What is the first derivative of (e^{-x}/(x+1)) ?
The first derivative of (e^{-x}/(x+1)) is (-e^{-x}x-2e^{-x})/((x+1)^2)