derivative of (e^{2x}^{sec(x)})

解

\frac{d}{d x} ((e^{2 x})^{s e c (x)})

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

解答ステップ

\frac{d}{d x} ((e^{2 x})^{s e c (x)})

簡素化

(e^{2 x})^{s e c (x)} : e^{2 x s e c (x)}

= \frac{d}{d x} (e^{2 x s e c (x)})

連鎖法則を適用:

e^{2 x s e c (x)} \frac{d}{d x} (2 x sec (x))

= e^{2 x s e c (x)} \frac{d}{d x} (2 x sec (x))

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

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