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

解

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

\frac{x}{x ^{2} + y ^{2} + z ^{2}}

解答ステップ

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

連鎖法則を適用:

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

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

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

= \frac{1}{2 x ^{2} + y ^{2} + z ^{2}} \cdot 2 x

簡素化

\frac{1}{2 x ^{2} + y ^{2} + z ^{2}} \cdot 2 x : \frac{x}{x ^{2} + y ^{2} + z ^{2}}

= \frac{x}{x ^{2} + y ^{2} + z ^{2}}