d/(dv)((\sqrt[3]{v}-2ve^v)/v)

Lösung

\frac{d}{d v} (\frac{3 v - 2 v e ^{v}}{v})

\frac{- 6 e ^{v} v ^{2} + v ^{\frac{1}{3}} - 3 3 v}{3 v ^{2}}

Schritte zur Lösung

\frac{d}{d v} (\frac{3 v - 2 v e ^{v}}{v})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d v} ( 3 v - 2 v e ^{v} ) v - \frac{d v}{d v} ( 3 v - 2 v e ^{v} )}{v ^{2}}

\frac{d}{d v} (3 v - 2 v e^{v}) = \frac{1 - 6 e ^{v} v ^{\frac{2}{3}} - 6 e ^{v} v ^{\frac{5}{3}}}{3 v ^{\frac{2}{3}}}

\frac{d v}{d v} = 1

= \frac{\frac{1 - 6 e ^{v} v ^{\frac{2}{3}} - 6 e ^{v} v ^{\frac{5}{3}}}{3 v ^{\frac{2}{3}}} v - 1 \cdot ( 3 v - 2 v e ^{v} )}{v ^{2}}

Vereinfache

\frac{\frac{1 - 6 e ^{v} v ^{\frac{2}{3}} - 6 e ^{v} v ^{\frac{5}{3}}}{3 v ^{\frac{2}{3}}} v - 1 \cdot ( 3 v - 2 v e ^{v} )}{v ^{2}} : \frac{- 6 e ^{v} v ^{2} + v ^{\frac{1}{3}} - 3 3 v}{3 v ^{2}}

= \frac{- 6 e ^{v} v ^{2} + v ^{\frac{1}{3}} - 3 3 v}{3 v ^{2}}

t an g e n t y = 5 x^{2} - x^{3}, (1, 4)

x \to 2 lim (\frac{2}{x})

\int 8 x + cos (x) d x

t a y l or e^{3 x}, 9

\frac{\partial}{\partial x} (sin (x) cos (4 y))