derivative of sec(2x+tan(2x))

解

\frac{d}{d x} (sec (2 x) + tan (2 x))

sec (2 x) tan (2 x) \cdot 2 + sec^{2} (2 x) \cdot 2

解答ステップ

\frac{d}{d x} (sec (2 x) + tan (2 x))

和/差の法則を適用:

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

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

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

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

= sec (2 x) tan (2 x) \cdot 2 + sec^{2} (2 x) \cdot 2