derivative of cos^2(sqrt(x))

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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