d/(dv)((p)(p+(1.3)/(v^2))(v-9))

Lösung

\frac{d}{d v} ((p (v)) (p (v) + \frac{1.3}{v ^{2}}) (v - 9))

2 v p \frac{d p}{d v} - 18 p \frac{d p}{d v} + \frac{1.3 \frac{d p}{d v}}{v} + \frac{- 1.3 p - 11.7 \frac{d p}{d v}}{v ^{2}} + \frac{23.4 p}{v ^{3}} + p^{2}

Schritte zur Lösung

\frac{d}{d v} ((p) (p + \frac{1.3}{v ^{2}}) (v - 9))

Wende die Produktregel an:

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

f = p, g = (p + \frac{1.3}{v ^{2}}) (v - 9)

= \frac{d p}{d v} (p + \frac{1.3}{v ^{2}}) (v - 9) + \frac{d}{d v} ((p + \frac{1.3}{v ^{2}}) (v - 9)) p

\frac{d}{d v} ((p + \frac{1.3}{v ^{2}}) (v - 9)) = v \frac{d p}{d v} - 9 \frac{d p}{d v} - \frac{1.3}{v ^{2}} + \frac{23.4}{v ^{3}} + p

= \frac{d p}{d v} (p + \frac{1.3}{v ^{2}}) (v - 9) + (v \frac{d p}{d v} - 9 \frac{d p}{d v} - \frac{1.3}{v ^{2}} + \frac{23.4}{v ^{3}} + p) p

Vereinfache

\frac{d p}{d v} (p + \frac{1.3}{v ^{2}}) (v - 9) + (v \frac{d p}{d v} - 9 \frac{d p}{d v} - \frac{1.3}{v ^{2}} + \frac{23.4}{v ^{3}} + p) p : 2 v p \frac{d p}{d v} - 18 p \frac{d p}{d v} + \frac{1.3 \frac{d p}{d v}}{v} + \frac{- 1.3 p - 11.7 \frac{d p}{d v}}{v ^{2}} + \frac{23.4 p}{v ^{3}} + p^{2}

= 2 v p \frac{d p}{d v} - 18 p \frac{d p}{d v} + \frac{1.3 \frac{d p}{d v}}{v} + \frac{- 1.3 p - 11.7 \frac{d p}{d v}}{v ^{2}} + \frac{23.4 p}{v ^{3}} + p^{2}

e x p an d - \frac{1}{( s - 1 ) ( s - 2 )}

s im pl i f y (cos (x)) (2 + cos (x))

e x p an d \frac{18 x}{( 9 - x ^{2} ) ^{2}}

e x p an d \frac{( sin ( a ) + tan ( a ) ) cot ( a )}{csc ( a ) + cot ( a )}

s im pl i f y 6 (7 - 2)