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

The answer to (\partial)/(\partial x)(e^{x/y}) is (e^{x/y})/y

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{\frac{x}{y}} \frac{1}{y}

Simplify

e^{\frac{x}{y}} \frac{1}{y} : \frac{e ^{\frac{x}{y}}}{y}

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

\frac{\partial}{\partial r} (r sin (t) sin (x))

\int_{0}^{1} \frac{17}{4 y - 1} d y

\frac{6}{s} + 8 a \cdot \frac{s}{s ^{2} + 16}

\frac{d}{d x} (4 x^{4} + \frac{1}{3} x^{3} + x + 1)

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