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

解

\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)

解答ステップ

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

C

を定数として扱う

積の法則を適用:

(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)