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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

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}

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

Simplify

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

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

x^{2} - 2

\int \frac{y ^{2} + 6 y + 9}{( y ^{2} + 9 ) ^{2}} d y

f (x) = 3 x - 1, at x = 5

n = 1 \sum \infty \frac{n !}{( 2 n ) !}

x^{4} + \frac{4}{3} x^{3} - 4 x^{2} - \frac{4}{3}

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