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

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

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

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

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

Solution steps

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

Treat

y

as a constant

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}}

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

Simplify

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

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

\int x^{2} + 3 d x

\int_{0}^{1} \frac{2}{3} x^{2} (x + 1) d x

\frac{tan ( x ) - 20}{sec ( x )}

\int 4 (tan^{2} (x) + tan^{4} (x)) d x

y^{^{''}} - 6 y^{^{'}} + 5 y = 0

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