d/(dv)((p)((p+6.9v^2)(v-3.1)))

Lösung

\frac{d}{d v} ((p (v)) ((p (v) + 6.9 v^{2}) (v - 3.1)))

6.9 v^{3} \frac{d p}{d v} - 21.39 v^{2} \frac{d p}{d v} + 20.7 v^{2} p + 2 v p \frac{d p}{d v} - 42.78 v p - 6.2 p \frac{d p}{d v} + p^{2}

Schritte zur Lösung

\frac{d}{d v} ((p) ((p + 6.9 v^{2}) (v - 3.1)))

Wende die Produktregel an:

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

f = p, g = (p + 6.9 v^{2}) (v - 3.1)

= \frac{d p}{d v} (p + 6.9 v^{2}) (v - 3.1) + \frac{d}{d v} ((p + 6.9 v^{2}) (v - 3.1)) p

\frac{d}{d v} ((p + 6.9 v^{2}) (v - 3.1)) = 20.7 v^{2} + v \frac{d p}{d v} - 42.78 v - 3.1 \frac{d p}{d v} + p

= \frac{d p}{d v} (p + 6.9 v^{2}) (v - 3.1) + (20.7 v^{2} + v \frac{d p}{d v} - 42.78 v - 3.1 \frac{d p}{d v} + p) p

Vereinfache

\frac{d p}{d v} (p + 6.9 v^{2}) (v - 3.1) + (20.7 v^{2} + v \frac{d p}{d v} - 42.78 v - 3.1 \frac{d p}{d v} + p) p : 6.9 v^{3} \frac{d p}{d v} - 21.39 v^{2} \frac{d p}{d v} + 20.7 v^{2} p + 2 v p \frac{d p}{d v} - 42.78 v p - 6.2 p \frac{d p}{d v} + p^{2}

= 6.9 v^{3} \frac{d p}{d v} - 21.39 v^{2} \frac{d p}{d v} + 20.7 v^{2} p + 2 v p \frac{d p}{d v} - 42.78 v p - 6.2 p \frac{d p}{d v} + p^{2}

e x p an d \frac{3 ( 8 π - 9 3 )}{64}

\frac{d}{d t} ((s) (9 + 0.02 s))

e x p an d (3 + 2) (3 + 2)

s im pl i f y 2 + \frac{1}{12} (8.1 - 8) - \frac{\frac{1}{144} ( 8.1 - 8 ) ^{2}}{2}

e x p an d \frac{3 s + 7}{s ( s + 2 )}