derivative of 3|sin(xx|-4|cos(x)|)

解

\frac{d}{d x} (3 ∣ sin (x) x ∣ - 4 ∣ cos (x) ∣)

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

解答ステップ

\frac{d}{d x} (3 ∣ sin (x) x ∣ - 4 ∣ cos (x) ∣)

簡素化

3 ∣ sin (x) x ∣ - 4 ∣ cos (x) ∣ : 3 ∣ x ∣ ∣ sin (x) ∣ - 4 ∣ cos (x) ∣

= \frac{d}{d x} (3 ∣ x ∣ ∣ sin (x) ∣ - 4 ∣ cos (x) ∣)

和/差の法則を適用:

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

= \frac{d}{d x} (3 ∣ x ∣ ∣ sin (x) ∣) - \frac{d}{d x} (4 ∣ cos (x) ∣)

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

\frac{d}{d x} (4 ∣ cos (x) ∣) = - \frac{2 sin ( 2 x )}{∣ cos ( x ) ∣}

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

簡素化

= 3 (\frac{x ∣ sin ( x ) ∣}{∣ x ∣} + \frac{sin ( x ) cos ( x ) ∣ x ∣}{∣ sin ( x ) ∣}) + \frac{2 sin ( 2 x )}{∣ cos ( x ) ∣}