derivative of cos(xcot(x))

解

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

- cos (x) - cot (x) csc (x)

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (x), g = cot (x)

= \frac{d}{d x} (cos (x)) cot (x) + \frac{d}{d x} (cot (x)) cos (x)

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

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

= (- sin (x)) cot (x) + (- csc^{2} (x)) cos (x)

簡素化

(- sin (x)) cot (x) + (- csc^{2} (x)) cos (x) : - cos (x) - cot (x) csc (x)

= - cos (x) - cot (x) csc (x)