d/(dM)((R(M,C))(M^2(C/2-M/3)))

Lösung

\frac{d}{d M} ((R (M, C)) (M^{2} (\frac{C}{2} - \frac{M}{3})))

\frac{d}{d M} (R (M, C)) M^{2} (\frac{C}{2} - \frac{M}{3}) + (CM - M^{2}) R (M, C)

Schritte zur Lösung

\frac{d}{d M} ((R (M, C)) (M^{2} (\frac{C}{2} - \frac{M}{3})))

Behandle

C

als Konstante

Wende die Produktregel an:

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

f = R (M, C), g = M^{2} (\frac{C}{2} - \frac{M}{3})

= \frac{d}{d M} (R (M, C)) M^{2} (\frac{C}{2} - \frac{M}{3}) + \frac{d}{d M} (M^{2} (\frac{C}{2} - \frac{M}{3})) R (M, C)

\frac{d}{d M} (M^{2} (\frac{C}{2} - \frac{M}{3})) = CM - M^{2}

= \frac{d}{d M} (R (M, C)) M^{2} (\frac{C}{2} - \frac{M}{3}) + (CM - M^{2}) R (M, C)

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