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

The d/(dy)(y-y/(x^2)e^{y/x}) is 1-(e^{y/x}y+xe^{y/x})/(x^3)

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

The first d/(dy)(y-y/(x^2)e^{y/x}) is 1-(e^{y/x}y+xe^{y/x})/(x^3)

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

1 - \frac{e ^{\frac{y}{x}} y + x e ^{\frac{y}{x}}}{x ^{3}}

Solution steps

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

Simplify

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

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d y}{d y} = 1

\frac{d}{d y} (\frac{e ^{\frac{y}{x}} y}{x ^{2}}) = \frac{e ^{\frac{y}{x}} y + x e ^{\frac{y}{x}}}{x ^{3}}

= 1 - \frac{e ^{\frac{y}{x}} y + x e ^{\frac{y}{x}}}{x ^{3}}

5 sin (\frac{π}{4})

\frac{d}{d x} (\frac{y}{x - y})

f (x) = \frac{1}{3 + 2 x}, (2, \frac{1}{7})

\int 3 sin^{3} (x) cos^{5} (x) d x

\frac{8 x ^{2} + 6 x + 2}{x}

What is the d/(dy)(y-y/(x^2)e^{y/x}) ?
The d/(dy)(y-y/(x^2)e^{y/x}) is 1-(e^{y/x}y+xe^{y/x})/(x^3)
What is the first d/(dy)(y-y/(x^2)e^{y/x}) ?
The first d/(dy)(y-y/(x^2)e^{y/x}) is 1-(e^{y/x}y+xe^{y/x})/(x^3)