What is the derivative of (e^{2x})/(x+1) ?

The derivative of (e^{2x})/(x+1) is (2e^{2x}x+e^{2x})/((x+1)^2)

What is the first derivative of (e^{2x})/(x+1) ?

The first derivative of (e^{2x})/(x+1) is (2e^{2x}x+e^{2x})/((x+1)^2)

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derivative of

\frac{e ^{2 x}}{x + 1}

\frac{2 e ^{2 x} x + e ^{2 x}}{( x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{2 x}}{x + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{2 x} ) ( x + 1 ) - \frac{d}{d x} ( x + 1 ) e ^{2 x}}{( x + 1 ) ^{2}}

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

\frac{d}{d x} (x + 1) = 1

= \frac{e ^{2 x} \cdot 2 ( x + 1 ) - 1 \cdot e ^{2 x}}{( x + 1 ) ^{2}}

Simplify

\frac{e ^{2 x} \cdot 2 ( x + 1 ) - 1 \cdot e ^{2 x}}{( x + 1 ) ^{2}} : \frac{2 e ^{2 x} x + e ^{2 x}}{( x + 1 ) ^{2}}

= \frac{2 e ^{2 x} x + e ^{2 x}}{( x + 1 ) ^{2}}

n = 6 \sum \infty \frac{1}{n ^{3}}

\int \frac{1}{8 x} d x

\frac{d y}{d x} = \frac{x ^{6} - 2 y}{x}

\frac{\partial}{\partial y} (x y^{2} cos (2 + x^{2} y))

\frac{2}{( s - 2 )}

What is the derivative of (e^{2x})/(x+1) ?
The derivative of (e^{2x})/(x+1) is (2e^{2x}x+e^{2x})/((x+1)^2)
What is the first derivative of (e^{2x})/(x+1) ?
The first derivative of (e^{2x})/(x+1) is (2e^{2x}x+e^{2x})/((x+1)^2)