derivative y=sqrt(x^2-x+9)

解

導関数

y = x^{2} - x + 9

\frac{2 x - 1}{2 x ^{2} - x + 9}

解答ステップ

\frac{d}{d x} (x^{2} - x + 9)

連鎖法則を適用:

\frac{1}{2 x ^{2} - x + 9} \frac{d}{d x} (x^{2} - x + 9)

= \frac{1}{2 x ^{2} - x + 9} \frac{d}{d x} (x^{2} - x + 9)

\frac{d}{d x} (x^{2} - x + 9) = 2 x - 1

= \frac{1}{2 x ^{2} - x + 9} (2 x - 1)

簡素化

\frac{1}{2 x ^{2} - x + 9} (2 x - 1) : \frac{2 x - 1}{2 x ^{2} - x + 9}

= \frac{2 x - 1}{2 x ^{2} - x + 9}