What is (\partial}{\partial x}(\frac{xe^x)/y) ?

The answer to (\partial}{\partial x}(\frac{xe^x)/y) is (e^x+e^xx)/y

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(\partial}{\partial x}(\frac{xe^x)/y)

\frac{\partial}{\partial x} (\frac{x e ^{x}}{y})

\frac{e ^{x} + e ^{x} x}{y}

Solution steps

\frac{\partial}{\partial x} (\frac{x e ^{x}}{y})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{y} \frac{\partial}{\partial x} (x e^{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x}

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (e^{x}) = e^{x}

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

Simplify

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

= \frac{e ^{x} + e ^{x} x}{y}

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What is (\partial}{\partial x}(\frac{xe^x)/y) ?
The answer to (\partial}{\partial x}(\frac{xe^x)/y) is (e^x+e^xx)/y