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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

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

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

\frac{d}{d x} (cos (10 x) - 0.1 sin (10 x))

\int \frac{2}{x ^{2} + 3} d x

(x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}}) d x + (x^{3} y^{2}) d y = 0

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