d/(dv)(sqrt(u/v))

Lösung

\frac{d}{d v} (\frac{u}{v})

- \frac{u}{2 v ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d v} (\frac{u}{v})

Behandle

u

als Konstante

Wende die Kettenregel an:

\frac{1}{2 \frac{u}{v}} \frac{d}{d v} (\frac{u}{v})

= \frac{1}{2 \frac{u}{v}} \frac{d}{d v} (\frac{u}{v})

\frac{d}{d v} (\frac{u}{v}) = - \frac{u}{v ^{2}}

= \frac{1}{2 \frac{u}{v}} (- \frac{u}{v ^{2}})

Vereinfache

\frac{1}{2 \frac{u}{v}} (- \frac{u}{v ^{2}}) : - \frac{u}{2 v ^{\frac{3}{2}}}

= - \frac{u}{2 v ^{\frac{3}{2}}}

\frac{\partial}{\partial y} (- x e^{- 3 x y})

\int x e^{m x} d x

x \to 0 lim (\frac{e ^{5 x} - 1}{x})

\int cos (5 x) sin (x) sin (8 x) d x

\frac{d y}{d x} = \frac{x cos ( x ^{2} )}{4 y}