derivative of sin(x+cos(x)+tan(x))

解

\frac{d}{d x} (sin (x) + cos (x) + tan (x))

cos (x) - sin (x) + sec^{2} (x)

解答ステップ

\frac{d}{d x} (sin (x) + cos (x) + tan (x))

和/差の法則を適用:

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

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

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

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= cos (x) - sin (x) + sec^{2} (x)