What is the derivative of (e^x/(5+e^x)) ?

The derivative of (e^x/(5+e^x)) is (5e^x)/((5+e^x)^2)

What is the first derivative of (e^x/(5+e^x)) ?

The first derivative of (e^x/(5+e^x)) is (5e^x)/((5+e^x)^2)

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\frac{d}{d x} (\frac{e ^{x}}{5 + e ^{x}})

\frac{5 e ^{x}}{( 5 + e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{5 + 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} ) ( 5 + e ^{x} ) - \frac{d}{d x} ( 5 + e ^{x} ) e ^{x}}{( 5 + e ^{x} ) ^{2}}

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

\frac{d}{d x} (5 + e^{x}) = e^{x}

= \frac{e ^{x} ( 5 + e ^{x} ) - e ^{x} e ^{x}}{( 5 + e ^{x} ) ^{2}}

Simplify

\frac{e ^{x} ( 5 + e ^{x} ) - e ^{x} e ^{x}}{( 5 + e ^{x} ) ^{2}} : \frac{5 e ^{x}}{( 5 + e ^{x} ) ^{2}}

= \frac{5 e ^{x}}{( 5 + e ^{x} ) ^{2}}

\frac{\partial}{\partial y} (2 x - 5 y + 3)

\int (1 + e^{x} y + x e^{x} y) d x

\int_{1}^{\infty} x e^{- 2 x} d x

\frac{d}{d x} (a x^{2} e^{- 4 x})

\frac{3 d y}{d x} + 12 y = 4

What is the derivative of (e^x/(5+e^x)) ?
The derivative of (e^x/(5+e^x)) is (5e^x)/((5+e^x)^2)
What is the first derivative of (e^x/(5+e^x)) ?
The first derivative of (e^x/(5+e^x)) is (5e^x)/((5+e^x)^2)