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

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

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

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

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derivative of

\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}}

x^{3} + 4 y^{2} = 12, (2, - 1)

\frac{d y}{d x} = x - \frac{y}{x}

y^{^{'}} + 5 y = 4

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

f (y) = arcsin (y^{2})

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