derivative of sqrt(3x^2-4x+6)

解

\frac{d}{d x} (3 x^{2} - 4 x + 6)

\frac{3 x - 2}{3 x ^{2} - 4 x + 6}

解答ステップ

\frac{d}{d x} (3 x^{2} - 4 x + 6)

連鎖法則を適用:

\frac{1}{2 3 x ^{2} - 4 x + 6} \frac{d}{d x} (3 x^{2} - 4 x + 6)

= \frac{1}{2 3 x ^{2} - 4 x + 6} \frac{d}{d x} (3 x^{2} - 4 x + 6)

\frac{d}{d x} (3 x^{2} - 4 x + 6) = 6 x - 4

= \frac{1}{2 3 x ^{2} - 4 x + 6} (6 x - 4)

簡素化

\frac{1}{2 3 x ^{2} - 4 x + 6} (6 x - 4) : \frac{3 x - 2}{3 x ^{2} - 4 x + 6}

= \frac{3 x - 2}{3 x ^{2} - 4 x + 6}