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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\frac{d}{d x} (\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}}

\int - 14 x^{- 4} y^{6} + 16 x^{- 5} y^{7} d y

\int \frac{x ^{2} + 2 x y - y ^{2}}{( x + y ) ^{2}} d x

y^{^{''}} - 14 y^{^{'}} + 51 y = 0

x y^{^{'}} + y = - 8 x y^{2}, y (1) = 1

\int \frac{7 x}{x ^{2} + 4} 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)