d/(dt)(sqrt(20-25sin^2(t)))

解

\frac{d}{d t} (20 - 25 sin^{2} (t))

- \frac{25 sin ( 2 t )}{2 20 - 25 sin ^{2} ( t )}

解答ステップ

\frac{d}{d t} (20 - 25 sin^{2} (t))

連鎖法則を適用:

\frac{1}{2 20 - 25 sin ^{2} ( t )} \frac{d}{d t} (20 - 25 sin^{2} (t))

= \frac{1}{2 20 - 25 sin ^{2} ( t )} \frac{d}{d t} (20 - 25 sin^{2} (t))

\frac{d}{d t} (20 - 25 sin^{2} (t)) = - 25 sin (2 t)

= \frac{1}{2 20 - 25 sin ^{2} ( t )} (- 25 sin (2 t))

簡素化

\frac{1}{2 20 - 25 sin ^{2} ( t )} (- 25 sin (2 t)) : - \frac{25 sin ( 2 t )}{2 20 - 25 sin ^{2} ( t )}

= - \frac{25 sin ( 2 t )}{2 20 - 25 sin ^{2} ( t )}