What is the derivative of (e^x/(3+e^x)) ?

The derivative of (e^x/(3+e^x)) is (3e^x)/((3+e^x)^2)

What is the first derivative of (e^x/(3+e^x)) ?

The first derivative of (e^x/(3+e^x)) is (3e^x)/((3+e^x)^2)

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\frac{d}{d x} (\frac{e ^{x}}{3 + e ^{x}})

\frac{3 e ^{x}}{( 3 + e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{3 + 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} ) ( 3 + e ^{x} ) - \frac{d}{d x} ( 3 + e ^{x} ) e ^{x}}{( 3 + e ^{x} ) ^{2}}

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

\frac{d}{d x} (3 + e^{x}) = e^{x}

= \frac{e ^{x} ( 3 + e ^{x} ) - e ^{x} e ^{x}}{( 3 + e ^{x} ) ^{2}}

Simplify

\frac{e ^{x} ( 3 + e ^{x} ) - e ^{x} e ^{x}}{( 3 + e ^{x} ) ^{2}} : \frac{3 e ^{x}}{( 3 + e ^{x} ) ^{2}}

= \frac{3 e ^{x}}{( 3 + e ^{x} ) ^{2}}

\frac{d}{d x} (7 sin (x) - 2 x^{3})

\int \frac{x ^{2} + 36 x + 36}{x ^{3} - 4 x} d x

x \to 1 lim (\frac{x - 1}{ln ( x )})

\frac{d}{d x} ((2 x^{2} + 3) (5 x + 3))

121 y^{^{''}} - 64 y = 0

What is the derivative of (e^x/(3+e^x)) ?
The derivative of (e^x/(3+e^x)) is (3e^x)/((3+e^x)^2)
What is the first derivative of (e^x/(3+e^x)) ?
The first derivative of (e^x/(3+e^x)) is (3e^x)/((3+e^x)^2)