derivative sqrt(r^2-9x^2)

解

導関数

r^{2} - 9 x^{2}

- \frac{9 x}{r ^{2} - 9 x ^{2}}

解答ステップ

\frac{d}{d x} (r^{2} - 9 x^{2})

連鎖法則を適用:

\frac{1}{2 r ^{2} - 9 x ^{2}} \frac{d}{d x} (r^{2} - 9 x^{2})

= \frac{1}{2 r ^{2} - 9 x ^{2}} \frac{d}{d x} (r^{2} - 9 x^{2})

\frac{d}{d x} (r^{2} - 9 x^{2}) = - 18 x

= \frac{1}{2 r ^{2} - 9 x ^{2}} (- 18 x)

簡素化

\frac{1}{2 r ^{2} - 9 x ^{2}} (- 18 x) : - \frac{9 x}{r ^{2} - 9 x ^{2}}

= - \frac{9 x}{r ^{2} - 9 x ^{2}}