derivative m^2(c/2-m/3)

解

導関数

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

c m - m^{2}

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d m} (m^{2}) = 2 m

\frac{d}{d m} (\frac{c}{2} - \frac{m}{3}) = - \frac{1}{3}

= 2 m (\frac{c}{2} - \frac{m}{3}) + (- \frac{1}{3}) m^{2}

簡素化

2 m (\frac{c}{2} - \frac{m}{3}) + (- \frac{1}{3}) m^{2} : c m - m^{2}

= c m - m^{2}