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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

d er i v a t i v e f (x) = (x - \frac{2}{x})

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

n = 1 \sum \infty ln (n)

x \to b lim (7 (- 7))

\frac{d x}{d t} = \frac{1}{x e ^{t + 2 x}}

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