d/(dv)((p)(p+6/(v^2))(v-1.1))

Lösung

\frac{d}{d v} ((p (v)) (p (v) + \frac{6}{v ^{2}}) (v - 1.1))

2 v p \frac{d p}{d v} - 2.2 p \frac{d p}{d v} + \frac{6 \frac{d p}{d v}}{v} + \frac{- 6 p - 6.6 \frac{d p}{d v}}{v ^{2}} + \frac{13.2 p}{v ^{3}} + p^{2}

Schritte zur Lösung

\frac{d}{d v} ((p) (p + \frac{6}{v ^{2}}) (v - 1.1))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = p, g = (p + \frac{6}{v ^{2}}) (v - 1.1)

= \frac{d p}{d v} (p + \frac{6}{v ^{2}}) (v - 1.1) + \frac{d}{d v} ((p + \frac{6}{v ^{2}}) (v - 1.1)) p

\frac{d}{d v} ((p + \frac{6}{v ^{2}}) (v - 1.1)) = v \frac{d p}{d v} - 1.1 \frac{d p}{d v} - \frac{6}{v ^{2}} + \frac{13.2}{v ^{3}} + p

= \frac{d p}{d v} (p + \frac{6}{v ^{2}}) (v - 1.1) + (v \frac{d p}{d v} - 1.1 \frac{d p}{d v} - \frac{6}{v ^{2}} + \frac{13.2}{v ^{3}} + p) p

Vereinfache

\frac{d p}{d v} (p + \frac{6}{v ^{2}}) (v - 1.1) + (v \frac{d p}{d v} - 1.1 \frac{d p}{d v} - \frac{6}{v ^{2}} + \frac{13.2}{v ^{3}} + p) p : 2 v p \frac{d p}{d v} - 2.2 p \frac{d p}{d v} + \frac{6 \frac{d p}{d v}}{v} + \frac{- 6 p - 6.6 \frac{d p}{d v}}{v ^{2}} + \frac{13.2 p}{v ^{3}} + p^{2}

= 2 v p \frac{d p}{d v} - 2.2 p \frac{d p}{d v} + \frac{6 \frac{d p}{d v}}{v} + \frac{- 6 p - 6.6 \frac{d p}{d v}}{v ^{2}} + \frac{13.2 p}{v ^{3}} + p^{2}

e x p an d \frac{π ( 2 + 2 + 10 )}{16}

s im pl i f y (\frac{6}{7} + w) (\frac{6}{7} - w)

e x p an d - \frac{x ( 1 + 2 x ^{2} + y ^{2} )}{y - 4 x ^{2} y - 4 y ^{3}}

e x p an d C (2, - 3)

e x p an d (3 x^{2} + \frac{x}{3})^{6}