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

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

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

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

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

Solution steps

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

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}}

\int (sin (3 x)) d x

\frac{\partial}{\partial x} (6 cos^{4} (3 x + 2))

\frac{d}{d x} (e^{2 x} + e^{- 2 x})

(x - 3)^{^{'}}

\frac{d}{d x} (x e^{\frac{x ^{2}}{2}})

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