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

解

導関数

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

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

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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