derivative of sqrt(12x-x^2)

解

\frac{d}{d x} (12 x - x^{2})

\frac{6 - x}{12 x - x ^{2}}

解答ステップ

\frac{d}{d x} (12 x - x^{2})

連鎖法則を適用:

\frac{1}{2 12 x - x ^{2}} \frac{d}{d x} (12 x - x^{2})

= \frac{1}{2 12 x - x ^{2}} \frac{d}{d x} (12 x - x^{2})

\frac{d}{d x} (12 x - x^{2}) = 12 - 2 x

= \frac{1}{2 12 x - x ^{2}} (12 - 2 x)

簡素化

\frac{1}{2 12 x - x ^{2}} (12 - 2 x) : \frac{6 - x}{12 x - x ^{2}}

= \frac{6 - x}{12 x - x ^{2}}