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

\int 2 (x + 1) d x

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = - 1, y^{^{'}} (0) = - 3

\int sin (x) cos (n x) d x

\frac{d y}{d x} y = 8 x

x \to 0 + lim (\frac{x}{x - 3})

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)