derivative of xln(y+sin(3x))

解

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

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

解答ステップ

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

和/差の法則を適用:

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

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

\frac{d}{d x} (x ln (y)) = ln (y) + \frac{x \frac{d y}{d x}}{y}

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

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