What is (\partial)/(\partial x)((e^x)/(1+e^x)) ?

The answer to (\partial)/(\partial x)((e^x)/(1+e^x)) is (e^x)/((1+e^x)^2)

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(\partial)/(\partial x)((e^x)/(1+e^x))

\frac{\partial}{\partial x} (\frac{e ^{x}}{1 + e ^{x}})

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

Solution steps

\frac{\partial}{\partial x} (\frac{e ^{x}}{1 + e ^{x}})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{1}{( x - 1 ) ( x + 2 ) ( x + 3 )} d x

\frac{\partial}{\partial x} (sin (π (4 x - 4 y)))

\frac{2}{x}

(\frac{x ^{3}}{x ^{8} + 7})^{2}

h \to 0 lim (h^{4} cos (\frac{3}{h}))

What is (\partial)/(\partial x)((e^x)/(1+e^x)) ?
The answer to (\partial)/(\partial x)((e^x)/(1+e^x)) is (e^x)/((1+e^x)^2)