derivative of sqrt(3-7x-x^2)

解

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

\frac{- 2 x - 7}{2 3 - 7 x - x ^{2}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{2 3 - 7 x - x ^{2}} (- 2 x - 7) : \frac{- 2 x - 7}{2 3 - 7 x - x ^{2}}

= \frac{- 2 x - 7}{2 3 - 7 x - x ^{2}}