d/(d{x)}(sqrt(1-{x)^2-{y}^2-{z}^2})

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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