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

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

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

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

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Popular >

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

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

Solution steps

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

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

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

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

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

Expand

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

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

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

\frac{\partial}{\partial x} (- 3 sin (x))

n = 2 \sum \infty \frac{1}{n ^{n}}

n \to \infty lim (n^{1})

\frac{\partial}{\partial x} (\frac{1}{( x ^{2} + y ^{2} + 1 )})

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