derivative of sqrt(cos(4x))

解

\frac{d}{d x} (cos (4 x))

- 2 sin (4 x) sec (4 x)

解答ステップ

\frac{d}{d x} (cos (4 x))

連鎖法則を適用:

\frac{1}{2 cos ( 4 x )} \frac{d}{d x} (cos (4 x))

= \frac{1}{2 cos ( 4 x )} \frac{d}{d x} (cos (4 x))

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= \frac{1}{2 cos ( 4 x )} (- sin (4 x) \cdot 4)

簡素化

\frac{1}{2 cos ( 4 x )} (- sin (4 x) \cdot 4) : - 2 sin (4 x) sec (4 x)

= - 2 sin (4 x) sec (4 x)