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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

\int sin^{3} (8 x) d x

[x + (x + sin^{2} (x))^{5}]^{3}

y = arctan (x - 2)

\int (a^{\frac{2}{3}} - x^{\frac{2}{3}})^{3} d x

\frac{1}{x - 1}, 9

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