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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

e^{\frac{x}{y}} (- \frac{x}{y ^{2}}) : - \frac{e ^{\frac{x}{y}} x}{y ^{2}}

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

\frac{d}{d x} (1 0^{t a n (2 x)})

y^{^{''}} + 16 y = sin (4 x)

\int \frac{cosh ( x )}{1 + sinh ( x )} d x

\int \frac{1}{( e ^{x} + 1 )} d x

\frac{d}{d x} (\frac{1 + sin ( x )}{cos ( x )})

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