derivative of tan(5-sin(2x))

解

\frac{d}{d x} (tan (5 - sin (2 x)))

- 2 sec^{2} (5 - sin (2 x)) cos (2 x)

解答ステップ

\frac{d}{d x} (tan (5 - sin (2 x)))

連鎖法則を適用:

sec^{2} (5 - sin (2 x)) \frac{d}{d x} (5 - sin (2 x))

= sec^{2} (5 - sin (2 x)) \frac{d}{d x} (5 - sin (2 x))

\frac{d}{d x} (5 - sin (2 x)) = - 2 cos (2 x)

= sec^{2} (5 - sin (2 x)) (- 2 cos (2 x))

簡素化

= - 2 sec^{2} (5 - sin (2 x)) cos (2 x)