derivative f(x)=|4+7x|

解

導関数

f (x) = ∣ 4 + 7 x ∣

\frac{7 ( 4 + 7 x )}{∣ 4 + 7 x ∣}

解答ステップ

\frac{d}{d x} (∣ 4 + 7 x ∣)

連鎖法則を適用:

\frac{4 + 7 x}{∣ ( 4 + 7 x ) ∣} \frac{d}{d x} (4 + 7 x)

= \frac{4 + 7 x}{∣ ( 4 + 7 x ) ∣} \frac{d}{d x} (4 + 7 x)

\frac{d}{d x} (4 + 7 x) = 7

= \frac{4 + 7 x}{∣ ( 4 + 7 x ) ∣} \cdot 7

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{7 ( 4 + 7 x )}{∣ 4 + 7 x ∣}