derivative 3(cos(x)ln(x)+(sin(x))/x)

解

導関数

3 (cos (x) ln (x) + \frac{sin ( x )}{x})

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

解答ステップ

\frac{d}{d x} (3 (cos (x) ln (x) + \frac{sin ( x )}{x}))

定数を除去:

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

= 3 \frac{d}{d x} (cos (x) ln (x) + \frac{sin ( x )}{x})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 3 (\frac{d}{d x} (cos (x) ln (x)) + \frac{d}{d x} (\frac{sin ( x )}{x}))

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

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

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

簡素化

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

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