(\partial)/(\partial x)(sqrt(1-x^2-y^2))

解

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

- \frac{x}{1 - x ^{2} - y ^{2}}

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

= - \frac{x}{1 - x ^{2} - y ^{2}}