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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x 8 - x^{2}

\int \frac{1}{( 4 + x ^{2} ) ^{\frac{3}{2}}} d x

\frac{\partial}{\partial x} (x^{4} + x y^{3})

x \to 0 + lim (\frac{e ^{x}}{x})

x \to 5 lim (8 x + 9)

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