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

The answer to (\partial}{\partial x}(\frac{e^x)/x) is (e^xx-e^x)/(x^2)

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

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

\frac{e ^{x} x - e ^{x}}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

= \frac{e ^{x} x - e ^{x}}{x ^{2}}

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What is (\partial}{\partial x}(\frac{e^x)/x) ?
The answer to (\partial}{\partial x}(\frac{e^x)/x) is (e^xx-e^x)/(x^2)