derivative of sqrt(r^2-x^2)

解

\frac{d}{d x} (r (x)^{2} - x^{2})

\frac{r \frac{d r}{d x} - x}{r ^{2} - x ^{2}}

解答ステップ

\frac{d}{d x} (r^{2} - x^{2})

連鎖法則を適用:

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

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

\frac{d}{d x} (r^{2} - x^{2}) = 2 r \frac{d r}{d x} - 2 x

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

簡素化

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

= \frac{r \frac{d r}{d x} - x}{r ^{2} - x ^{2}}