What is the derivative of (e^x)/(6+e^x) ?

The derivative of (e^x)/(6+e^x) is (6e^x)/((6+e^x)^2)

What is the first derivative of (e^x)/(6+e^x) ?

The first derivative of (e^x)/(6+e^x) is (6e^x)/((6+e^x)^2)

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derivative of

\frac{e ^{x}}{6 + e ^{x}}

\frac{6 e ^{x}}{( 6 + e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{6 + 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} ) ( 6 + e ^{x} ) - \frac{d}{d x} ( 6 + e ^{x} ) e ^{x}}{( 6 + e ^{x} ) ^{2}}

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

\frac{d}{d x} (6 + e^{x}) = e^{x}

= \frac{e ^{x} ( 6 + e ^{x} ) - e ^{x} e ^{x}}{( 6 + e ^{x} ) ^{2}}

Simplify

\frac{e ^{x} ( 6 + e ^{x} ) - e ^{x} e ^{x}}{( 6 + e ^{x} ) ^{2}} : \frac{6 e ^{x}}{( 6 + e ^{x} ) ^{2}}

= \frac{6 e ^{x}}{( 6 + e ^{x} ) ^{2}}

\frac{d}{d x} (\frac{1}{3 x - 4})

\frac{d}{d x} (2.2716 e^{0.2865 x})

\int x (x^{\frac{1}{3}} - x^{\frac{2}{5}}) d x

\int_{0}^{\infty} sin (x) d x

\frac{4 x + 1}{x}

What is the derivative of (e^x)/(6+e^x) ?
The derivative of (e^x)/(6+e^x) is (6e^x)/((6+e^x)^2)
What is the first derivative of (e^x)/(6+e^x) ?
The first derivative of (e^x)/(6+e^x) is (6e^x)/((6+e^x)^2)