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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derivative of

\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}}

\int_{- 2}^{3} ∣ x ∣ d x

\frac{d}{d x} (cos (x) + 2 x)

\int x e^{B - x} d x

\frac{6 x}{7 - cot ( x )}

x \to \infty lim (\frac{5}{0})

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)