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

Lösung

\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}}

Schritte zur Lösung

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

Vereinfache

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}})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

(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}}

d er i v a t i v e 5 sin (\frac{π}{4})

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

t an g e n t f (x) = \frac{1}{3 + 2 x}, (2, \frac{1}{7})

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

d er i v a t i v e \frac{8 x ^{2} + 6 x + 2}{x}