d/(dt)(tan(e^{2t})+e^{tan(2t)})

解

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

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

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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