What is the derivative of (e^x)/(8+e^x) ?

The derivative of (e^x)/(8+e^x) is (8e^x)/((8+e^x)^2)

What is the first derivative of (e^x)/(8+e^x) ?

The first derivative of (e^x)/(8+e^x) is (8e^x)/((8+e^x)^2)

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derivative of

\frac{e ^{x}}{8 + e ^{x}}

\frac{8 e ^{x}}{( 8 + e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{8 + 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} ) ( 8 + e ^{x} ) - \frac{d}{d x} ( 8 + e ^{x} ) e ^{x}}{( 8 + e ^{x} ) ^{2}}

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

\frac{d}{d x} (8 + e^{x}) = e^{x}

= \frac{e ^{x} ( 8 + e ^{x} ) - e ^{x} e ^{x}}{( 8 + e ^{x} ) ^{2}}

Simplify

\frac{e ^{x} ( 8 + e ^{x} ) - e ^{x} e ^{x}}{( 8 + e ^{x} ) ^{2}} : \frac{8 e ^{x}}{( 8 + e ^{x} ) ^{2}}

= \frac{8 e ^{x}}{( 8 + e ^{x} ) ^{2}}

\frac{d}{d x} (x + \frac{9}{x})

y = 9 + 3 x + 6 x e^{x}

\frac{d}{d x} (6 3 x^{2})

x \to \frac{1}{8} lim (\frac{1}{x} - x^{- 1})

\int x^{2} (x + 2) d x

What is the derivative of (e^x)/(8+e^x) ?
The derivative of (e^x)/(8+e^x) is (8e^x)/((8+e^x)^2)
What is the first derivative of (e^x)/(8+e^x) ?
The first derivative of (e^x)/(8+e^x) is (8e^x)/((8+e^x)^2)