derivative tan^2(3x)+1

解

導関数

tan^{2} (3 x) + 1

6 sec^{2} (3 x) tan (3 x)

解答ステップ

\frac{d}{d x} (tan^{2} (3 x) + 1)

簡素化

tan^{2} (3 x) + 1 : sec^{2} (3 x)

= \frac{d}{d x} (sec^{2} (3 x))

連鎖法則を適用:

2 sec (3 x) \frac{d}{d x} (sec (3 x))

= 2 sec (3 x) \frac{d}{d x} (sec (3 x))

\frac{d}{d x} (sec (3 x)) = sec (3 x) tan (3 x) \cdot 3

= 2 sec (3 x) sec (3 x) tan (3 x) \cdot 3

簡素化

2 sec (3 x) sec (3 x) tan (3 x) \cdot 3 : 6 sec^{2} (3 x) tan (3 x)

= 6 sec^{2} (3 x) tan (3 x)