What is the derivative of (xe^x/(x+1)) ?

The derivative of (xe^x/(x+1)) is (e^xx^2+e^xx+e^x)/((x+1)^2)

What is the first derivative of (xe^x/(x+1)) ?

The first derivative of (xe^x/(x+1)) is (e^xx^2+e^xx+e^x)/((x+1)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int (x^{2} - 3 x + 5) e^{x} d x

[x + (x + sin (2) (x))^{7}]^{3}

7 x - x^{2}

f (x) = \frac{3}{4} x + 7

\int - 3 cot (t) d t

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