What is the derivative of (e^x)/(e^x+3) ?

The derivative of (e^x)/(e^x+3) is (3e^x)/((e^x+3)^2)

What is the first derivative of (e^x)/(e^x+3) ?

The first derivative of (e^x)/(e^x+3) is (3e^x)/((e^x+3)^2)

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derivative of

\frac{e ^{x}}{e ^{x} + 3}

\frac{3 e ^{x}}{( e ^{x} + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{e ^{x} + 3})

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} + 3 ) - \frac{d}{d x} ( e ^{x} + 3 ) e ^{x}}{( e ^{x} + 3 ) ^{2}}

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

\frac{d}{d x} (e^{x} + 3) = e^{x}

= \frac{e ^{x} ( e ^{x} + 3 ) - e ^{x} e ^{x}}{( e ^{x} + 3 ) ^{2}}

Simplify

\frac{e ^{x} ( e ^{x} + 3 ) - e ^{x} e ^{x}}{( e ^{x} + 3 ) ^{2}} : \frac{3 e ^{x}}{( e ^{x} + 3 ) ^{2}}

= \frac{3 e ^{x}}{( e ^{x} + 3 ) ^{2}}

\frac{d y}{d x} = 2 x e^{- y}

\int \frac{4 x}{x ^{2} + 1} d x

\int x^{2} \cdot 2^{x} d x

f (x) = x + x^{\frac{2}{3}} - 3 x

x \to 0 lim (2 sin (x) ln (x))

What is the derivative of (e^x)/(e^x+3) ?
The derivative of (e^x)/(e^x+3) is (3e^x)/((e^x+3)^2)
What is the first derivative of (e^x)/(e^x+3) ?
The first derivative of (e^x)/(e^x+3) is (3e^x)/((e^x+3)^2)