derivative f(x)=(x+7)/(8x)

解

導関数

f (x) = \frac{x + 7}{8 x}

- \frac{7}{8 x ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x + 7}{8 x})

定数を除去:

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

= \frac{1}{8} \frac{d}{d x} (\frac{x + 7}{x})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (x + 7) = 1

\frac{d x}{d x} = 1

= \frac{1}{8} \cdot \frac{1 \cdot x - 1 \cdot ( x + 7 )}{x ^{2}}

簡素化

\frac{1}{8} \cdot \frac{1 \cdot x - 1 \cdot ( x + 7 )}{x ^{2}} : - \frac{7}{8 x ^{2}}

= - \frac{7}{8 x ^{2}}