derivative (h^2-2h+5)/8

解

導関数

\frac{h ^{2} - 2 h + 5}{8}

\frac{h - 1}{4}

解答ステップ

\frac{d}{d h} (\frac{h ^{2} - 2 h + 5}{8})

定数を除去:

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

= \frac{1}{8} \frac{d}{d h} (h^{2} - 2 h + 5)

和/差の法則を適用:

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

= \frac{1}{8} (\frac{d}{d h} (h^{2}) - \frac{d}{d h} (2 h) + \frac{d}{d h} (5))

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

\frac{d}{d h} (2 h) = 2

\frac{d}{d h} (5) = 0

= \frac{1}{8} (2 h - 2 + 0)

簡素化

\frac{1}{8} (2 h - 2 + 0) : \frac{h - 1}{4}

= \frac{h - 1}{4}