(\partial)/(\partial x)(sqrt(4-x^2-2y))

解

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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