derivative sqrt(r^2-15x^2)

解

導関数

r^{2} - 15 x^{2}

- \frac{15 x}{r ^{2} - 15 x ^{2}}

解答ステップ

\frac{d}{d x} (r^{2} - 15 x^{2})

連鎖法則を適用:

\frac{1}{2 r ^{2} - 15 x ^{2}} \frac{d}{d x} (r^{2} - 15 x^{2})

= \frac{1}{2 r ^{2} - 15 x ^{2}} \frac{d}{d x} (r^{2} - 15 x^{2})

\frac{d}{d x} (r^{2} - 15 x^{2}) = - 30 x

= \frac{1}{2 r ^{2} - 15 x ^{2}} (- 30 x)

簡素化

\frac{1}{2 r ^{2} - 15 x ^{2}} (- 30 x) : - \frac{15 x}{r ^{2} - 15 x ^{2}}

= - \frac{15 x}{r ^{2} - 15 x ^{2}}