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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int x (8 - 5 x^{2})^{3} d x

x^{3} - x

\frac{\partial}{\partial x} (\frac{3 x}{y ^{2}})

\int sin (4 x) cos (2 x) d x

\frac{d}{d x} (\frac{6 ( x - 3 ) ^{2}}{3 ( x ^{2} - 3 x - 4 )})

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