derivative f(x)=sec^5(x)

解

導関数

f (x) = sec^{5} (x)

5 sec^{5} (x) tan (x)

解答ステップ

\frac{d}{d x} (sec^{5} (x))

連鎖法則を適用:

5 (sec (x))^{4} \frac{d}{d x} (sec (x))

= 5 (sec (x))^{4} \frac{d}{d x} (sec (x))

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

= 5 (sec (x))^{4} sec (x) tan (x)

簡素化

5 sec^{4} (x) sec (x) tan (x) : 5 sec^{5} (x) tan (x)

= 5 sec^{5} (x) tan (x)