derivative 1/8 x^2-7x+16

解

導関数

\frac{1}{8} x^{2} - 7 x + 16

\frac{x}{4} - 7

解答ステップ

\frac{d}{d x} (\frac{1}{8} x^{2} - 7 x + 16)

簡素化

\frac{1}{8} x^{2} - 7 x + 16 : \frac{x ^{2}}{8} - 7 x + 16

= \frac{d}{d x} (\frac{x ^{2}}{8} - 7 x + 16)

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{x ^{2}}{8}) - \frac{d}{d x} (7 x) + \frac{d}{d x} (16)

\frac{d}{d x} (\frac{x ^{2}}{8}) = \frac{x}{4}

\frac{d}{d x} (7 x) = 7

\frac{d}{d x} (16) = 0

= \frac{x}{4} - 7 + 0

簡素化

= \frac{x}{4} - 7