derivative (v^3+1)/v

Lösung

ableitung von

\frac{v ^{3} + 1}{v}

\frac{2 v ^{3} - 1}{v ^{2}}

Schritte zur Lösung

\frac{d}{d v} (\frac{v ^{3} + 1}{v})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d v} ( v ^{3} + 1 ) v - \frac{d v}{d v} ( v ^{3} + 1 )}{v ^{2}}

\frac{d}{d v} (v^{3} + 1) = 3 v^{2}

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

= \frac{3 v ^{2} v - 1 \cdot ( v ^{3} + 1 )}{v ^{2}}

Vereinfache

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

= \frac{2 v ^{3} - 1}{v ^{2}}

l a pl a ce t r an s f or m f (t) = r^{2} + 6 r - 3

s l o p e (3.1) (6.3)

d er i v a t i v e - 2 x^{4} + 2 x^{3} - x^{2} + x

d er i v a t i v e y = 7 e^{x}

t an g e n t f (x) = 4 4 x + 2, at x = 1