derivative of cos^2(3sqrt(x))

解

\frac{d}{d x} (cos^{2} (3 x))

- \frac{3 cos ( 3 x ) sin ( 3 x )}{x}

解答ステップ

\frac{d}{d x} (cos^{2} (3 x))

連鎖法則を適用:

2 cos (3 x) \frac{d}{d x} (cos (3 x))

= 2 cos (3 x) \frac{d}{d x} (cos (3 x))

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \frac{3}{2 x}

= 2 cos (3 x) (- sin (3 x) \frac{3}{2 x})

簡素化

2 cos (3 x) (- sin (3 x) \frac{3}{2 x}) : - \frac{3 cos ( 3 x ) sin ( 3 x )}{x}

= - \frac{3 cos ( 3 x ) sin ( 3 x )}{x}