derivative of tan(e^{2x}+e^{tan(2x)})

解

\frac{d}{d x} (tan (e^{2 x}) + e^{t a n (2 x)})

sec^{2} (e^{2 x}) e^{2 x} \cdot 2 + e^{t a n (2 x)} sec^{2} (2 x) \cdot 2

解答ステップ

\frac{d}{d x} (tan (e^{2 x}) + e^{t a n (2 x)})

和/差の法則を適用:

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

= \frac{d}{d x} (tan (e^{2 x})) + \frac{d}{d x} (e^{t a n (2 x)})

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

\frac{d}{d x} (e^{t a n (2 x)}) = e^{t a n (2 x)} sec^{2} (2 x) \cdot 2

= sec^{2} (e^{2 x}) e^{2 x} \cdot 2 + e^{t a n (2 x)} sec^{2} (2 x) \cdot 2