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}

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\int \frac{56}{1 - cos ( 8 x )} d x

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