(\partial)/(\partial x)(sqrt(14-x^2-4xy))

解

\frac{\partial}{\partial x} (14 - x^{2} - 4 x y)

- \frac{x + 2 y}{- x ^{2} - 4 x y + 14}

解答ステップ

\frac{\partial}{\partial x} (14 - x^{2} - 4 x y)

y

を定数として扱う

連鎖法則を適用:

\frac{1}{2 14 - x ^{2} - 4 x y} \frac{\partial}{\partial x} (14 - x^{2} - 4 x y)

= \frac{1}{2 14 - x ^{2} - 4 x y} \frac{\partial}{\partial x} (14 - x^{2} - 4 x y)

\frac{\partial}{\partial x} (14 - x^{2} - 4 x y) = - 2 x - 4 y

= \frac{1}{2 14 - x ^{2} - 4 x y} (- 2 x - 4 y)

簡素化

\frac{1}{2 14 - x ^{2} - 4 x y} (- 2 x - 4 y) : - \frac{x + 2 y}{- x ^{2} - 4 x y + 14}

= - \frac{x + 2 y}{- x ^{2} - 4 x y + 14}