d/(dv)(1/2 a^2v+c)

解

\frac{d}{d v} (\frac{1}{2} a^{2} v + c)

\frac{a ^{2}}{2}

解答ステップ

\frac{d}{d v} (\frac{1}{2} a^{2} v + c)

簡素化

\frac{1}{2} a^{2} v + c : \frac{a ^{2} v}{2} + c

= \frac{d}{d v} (\frac{a ^{2} v}{2} + c)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d v} (\frac{a ^{2} v}{2}) + \frac{d}{d v} (c)

\frac{d}{d v} (\frac{a ^{2} v}{2}) = \frac{a ^{2}}{2}

\frac{d}{d v} (c) = 0

= \frac{a ^{2}}{2} + 0

簡素化

= \frac{a ^{2}}{2}