derivative (sin(2x)cos(3x))/x

解

導関数

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

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

解答ステップ

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

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

= \frac{( 2 cos ( 2 x ) cos ( 3 x ) - 3 sin ( 3 x ) sin ( 2 x ) ) x - 1 \cdot sin ( 2 x ) cos ( 3 x )}{x ^{2}}

簡素化

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