derivative ln(sec(5x)+tan(5x))

解

導関数

ln (sec (5 x) + tan (5 x))

5 sec (5 x)

解答ステップ

\frac{d}{d x} (ln (sec (5 x) + tan (5 x)))

連鎖法則を適用:

\frac{1}{sec ( 5 x ) + tan ( 5 x )} \frac{d}{d x} (sec (5 x) + tan (5 x))

= \frac{1}{sec ( 5 x ) + tan ( 5 x )} \frac{d}{d x} (sec (5 x) + tan (5 x))

\frac{d}{d x} (sec (5 x) + tan (5 x)) = sec (5 x) tan (5 x) \cdot 5 + sec^{2} (5 x) \cdot 5

= \frac{1}{sec ( 5 x ) + tan ( 5 x )} (sec (5 x) tan (5 x) \cdot 5 + sec^{2} (5 x) \cdot 5)

簡素化

\frac{1}{sec ( 5 x ) + tan ( 5 x )} (sec (5 x) tan (5 x) \cdot 5 + sec^{2} (5 x) \cdot 5) : 5 sec (5 x)

= 5 sec (5 x)