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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 1 lim (\frac{e ^{x - 1} - 1}{ln ^{2} ( x )})

x^{2} - 4 x + 3, 3 + 4 x - x^{2}

\int_{- 1}^{1} (x^{2} - 1) d x

\frac{\partial}{\partial z} (sin (x + 2 y + 3 z))

f (x) = 6 x^{2} (x - 9)

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