(\partial)/(\partial y)(sqrt(38-x^2-4y^2))

解

\frac{\partial}{\partial y} (38 - x^{2} - 4 y^{2})

- \frac{4 y}{38 - x ^{2} - 4 y ^{2}}

解答ステップ

\frac{\partial}{\partial y} (38 - x^{2} - 4 y^{2})

x

を定数として扱う

連鎖法則を適用:

\frac{1}{2 38 - x ^{2} - 4 y ^{2}} \frac{\partial}{\partial y} (38 - x^{2} - 4 y^{2})

= \frac{1}{2 38 - x ^{2} - 4 y ^{2}} \frac{\partial}{\partial y} (38 - x^{2} - 4 y^{2})

\frac{\partial}{\partial y} (38 - x^{2} - 4 y^{2}) = - 8 y

= \frac{1}{2 38 - x ^{2} - 4 y ^{2}} (- 8 y)

簡素化

\frac{1}{2 38 - x ^{2} - 4 y ^{2}} (- 8 y) : - \frac{4 y}{38 - x ^{2} - 4 y ^{2}}

= - \frac{4 y}{38 - x ^{2} - 4 y ^{2}}