d/(dm)(({r}(m))(m^2(c/2-m/3)))

Lösung

\frac{d}{d m} ((r (m)) (m^{2} (\frac{c}{2} - \frac{m}{3})))

\frac{d}{d m} (r (m)) m^{2} (\frac{c}{2} - \frac{m}{3}) + (c m - m^{2}) r (m)

Schritte zur Lösung

\frac{d}{d m} ((r (m)) (m^{2} (\frac{c}{2} - \frac{m}{3})))

Wende die Produktregel an:

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

f = r (m), g = m^{2} (\frac{c}{2} - \frac{m}{3})

= \frac{d}{d m} (r (m)) m^{2} (\frac{c}{2} - \frac{m}{3}) + \frac{d}{d m} (m^{2} (\frac{c}{2} - \frac{m}{3})) r (m)

\frac{d}{d m} (m^{2} (\frac{c}{2} - \frac{m}{3})) = c m - m^{2}

= \frac{d}{d m} (r (m)) m^{2} (\frac{c}{2} - \frac{m}{3}) + (c m - m^{2}) r (m)

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

s im pl i f y y (\frac{t}{5} - \frac{sin ( 5 t )}{25})

e x p an d A (2, 14) B (- 1, - 7)

e x p an d \frac{2}{3 ( 12 x ^{2} - 15 x - 24 )}

e x p an d (x - 5) (2 - x - x + 4)