derivative 8sqrt(7x^2+3)

解

導関数

8 7 x^{2} + 3

\frac{56 x}{7 x ^{2} + 3}

解答ステップ

\frac{d}{d x} (8 7 x^{2} + 3)

定数を除去:

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

= 8 \frac{d}{d x} (7 x^{2} + 3)

連鎖法則を適用:

\frac{1}{2 7 x ^{2} + 3} \frac{d}{d x} (7 x^{2} + 3)

= \frac{1}{2 7 x ^{2} + 3} \frac{d}{d x} (7 x^{2} + 3)

\frac{d}{d x} (7 x^{2} + 3) = 14 x

= 8 \cdot \frac{1}{2 7 x ^{2} + 3} \cdot 14 x

簡素化

8 \cdot \frac{1}{2 7 x ^{2} + 3} \cdot 14 x : \frac{56 x}{7 x ^{2} + 3}

= \frac{56 x}{7 x ^{2} + 3}