derivative sqrt(3x^2-x+1)

解

導関数

3 x^{2} - x + 1

\frac{6 x - 1}{2 3 x ^{2} - x + 1}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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