derivative of cos(x-y+ln(x+y))

解

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

- sin (x - y) (1 - \frac{d y}{d x}) + \frac{1 + \frac{d y}{d x}}{x + y}

解答ステップ

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

和/差の法則を適用:

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

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

\frac{d}{d x} (cos (x - y)) = - sin (x - y) (1 - \frac{d y}{d x})

\frac{d}{d x} (ln (x + y)) = \frac{1 + \frac{d y}{d x}}{x + y}

= - sin (x - y) (1 - \frac{d y}{d x}) + \frac{1 + \frac{d y}{d x}}{x + y}