derivative of (sin(2x)/(tan(x)))

解

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

- 2 sin (2 x)

解答ステップ

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

簡素化

\frac{sin ( 2 x )}{tan ( x )} : 2 cos^{2} (x)

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \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)) = - sin (x)

= 2 \cdot 2 cos (x) (- sin (x))

簡素化

2 \cdot 2 cos (x) (- sin (x)) : - 2 sin (2 x)

= - 2 sin (2 x)