What is the d/(dy)(e^{x/y}) ?

The d/(dy)(e^{x/y}) is -(e^{x/y}x)/(y^2)

What is the first d/(dy)(e^{x/y}) ?

The first d/(dy)(e^{x/y}) is -(e^{x/y}x)/(y^2)

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 6 lim (- \frac{1}{x - 6})

\frac{d y}{d x} = \frac{x ^{2} + 2 y}{x}

\int (\frac{x + 11}{x - 9}) d x

\int_{0}^{3} f (x) d x

\int x^{3} e^{- x^{4}} d x

What is the d/(dy)(e^{x/y}) ?
The d/(dy)(e^{x/y}) is -(e^{x/y}x)/(y^2)
What is the first d/(dy)(e^{x/y}) ?
The first d/(dy)(e^{x/y}) is -(e^{x/y}x)/(y^2)