derivative of tan(e^{7x}+e^{tan(7x)})

解

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

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

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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