derivative 1/3 pih^2(3r-h)

解

導関数

\frac{1}{3} π h^{2} (3 r - h)

π h^{2}

解答ステップ

\frac{d}{d r} (\frac{1}{3} π h^{2} (3 r - h))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{3} π h^{2} \frac{d}{d r} (3 r - h)

和/差の法則を適用:

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

= \frac{1}{3} π h^{2} (\frac{d}{d r} (3 r) - \frac{d h}{d r})

\frac{d}{d r} (3 r) = 3

\frac{d h}{d r} = 0

= \frac{1}{3} π h^{2} (3 - 0)

簡素化

\frac{1}{3} π h^{2} (3 - 0) : π h^{2}

= π h^{2}