derivative of (ax+b/c)

解

\frac{d}{d x} (\frac{a x + b}{c})

\frac{a}{c}

解答ステップ

\frac{d}{d x} (\frac{a x + b}{c})

定数を除去:

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

= \frac{1}{c} \frac{d}{d x} (a x + b)

和/差の法則を適用:

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

= \frac{1}{c} (\frac{d}{d x} (a x) + \frac{d b}{d x})

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

\frac{d b}{d x} = 0

= \frac{1}{c} (a + 0)

簡素化

\frac{1}{c} (a + 0) : \frac{a}{c}

= \frac{a}{c}