derivative of sec^{n-2}(x)

解

\frac{d}{d x} (sec^{n - 2} (x))

tan (x) sec^{n - 2} (x) (n - 2)

解答ステップ

\frac{d}{d x} (sec^{n - 2} (x))

連鎖法則を適用:

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

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

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

= (sec (x))^{n - 3} (n - 2) sec (x) tan (x)

簡素化

sec^{n - 3} (x) (n - 2) sec (x) tan (x) : tan (x) sec^{n - 2} (x) (n - 2)

= tan (x) sec^{n - 2} (x) (n - 2)