What is the derivative of (xe^x/(x^2+1)) ?

The derivative of (xe^x/(x^2+1)) is (e^xx^3-e^xx^2+e^xx+e^x)/((x^2+1)^2)

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

The first derivative of (xe^x/(x^2+1)) is (e^xx^3-e^xx^2+e^xx+e^x)/((x^2+1)^2)

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

\frac{e ^{x} x ^{3} - e ^{x} x ^{2} + e ^{x} x + e ^{x}}{( x ^{2} + 1 ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{( e ^{x} + e ^{x} x ) ( x ^{2} + 1 ) - 2 xx e ^{x}}{( x ^{2} + 1 ) ^{2}} : \frac{e ^{x} x ^{3} - e ^{x} x ^{2} + e ^{x} x + e ^{x}}{( x ^{2} + 1 ) ^{2}}

= \frac{e ^{x} x ^{3} - e ^{x} x ^{2} + e ^{x} x + e ^{x}}{( x ^{2} + 1 ) ^{2}}

\frac{d v}{d t} = \frac{( - 5 v - 29.4 )}{3}

\frac{d}{d x} (x^{- 3} ln (x))

\int_{0}^{3} 2 x d x

x \to \frac{1}{2} π lim (tan (x))

t \frac{d y}{d t} = t^{3} + 19 t^{3} y

What is the derivative of (xe^x/(x^2+1)) ?
The derivative of (xe^x/(x^2+1)) is (e^xx^3-e^xx^2+e^xx+e^x)/((x^2+1)^2)
What is the first derivative of (xe^x/(x^2+1)) ?
The first derivative of (xe^x/(x^2+1)) is (e^xx^3-e^xx^2+e^xx+e^x)/((x^2+1)^2)