What is the derivative of y=(e^x)/(1+e^x) ?

The derivative of y=(e^x)/(1+e^x) is (e^x)/((1+e^x)^2)

What is the first derivative of y=(e^x)/(1+e^x) ?

The first derivative of y=(e^x)/(1+e^x) is (e^x)/((1+e^x)^2)

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derivative of

y = \frac{e ^{x}}{1 + e ^{x}}

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

Solution steps

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

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

\frac{d}{d 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}}

\frac{d}{d x} (\frac{x ^{2} + 2 x - 23}{x - 4})

y = 9 cos (x)

\frac{x}{x + 2}

\frac{e ^{- s π}}{s ^{2} + 2 s + 2}

\int 7 csc (x) d x

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