(\partial)/(\partial y)(sqrt(16-x^2-4y))

解

\frac{\partial}{\partial y} (16 - x^{2} - 4 y)

- \frac{2}{16 - x ^{2} - 4 y}

解答ステップ

\frac{\partial}{\partial y} (16 - x^{2} - 4 y)

x

を定数として扱う

連鎖法則を適用:

\frac{1}{2 16 - x ^{2} - 4 y} \frac{\partial}{\partial y} (16 - x^{2} - 4 y)

= \frac{1}{2 16 - x ^{2} - 4 y} \frac{\partial}{\partial y} (16 - x^{2} - 4 y)

\frac{\partial}{\partial y} (16 - x^{2} - 4 y) = - 4

= \frac{1}{2 16 - x ^{2} - 4 y} (- 4)

簡素化

\frac{1}{2 16 - x ^{2} - 4 y} (- 4) : - \frac{2}{16 - x ^{2} - 4 y}

= - \frac{2}{16 - x ^{2} - 4 y}