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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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}}

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

Simplify

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

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

\int_{25}^{50} 20 d x

f (x) = \frac{x ^{2} + 1}{x + 4}

f (x) = x^{\frac{5}{2}} (2 - 5 x^{3})

e^{(- 2 x)} (3 x)^{2}

f (x) = - 5 sin (x), at x = \frac{π}{4}

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