derivative tan(e^{7t})+e^{tan(7t)}

解

導関数

tan (e^{7 t}) + e^{t a n (7 t)}

sec^{2} (e^{7 t}) e^{7 t} \cdot 7 + e^{t a n (7 t)} sec^{2} (7 t) \cdot 7

解答ステップ

\frac{d}{d t} (tan (e^{7 t}) + e^{t a n (7 t)})

和/差の法則を適用:

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

= \frac{d}{d t} (tan (e^{7 t})) + \frac{d}{d t} (e^{t a n (7 t)})

\frac{d}{d t} (tan (e^{7 t})) = sec^{2} (e^{7 t}) e^{7 t} \cdot 7

\frac{d}{d t} (e^{t a n (7 t)}) = e^{t a n (7 t)} sec^{2} (7 t) \cdot 7

= sec^{2} (e^{7 t}) e^{7 t} \cdot 7 + e^{t a n (7 t)} sec^{2} (7 t) \cdot 7