derivative 1/(cos^2(x))

解

導関数

\frac{1}{cos ^{2} ( x )}

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

解答ステップ

\frac{d}{d x} (\frac{1}{cos ^{2} ( x )})

簡素化

\frac{1}{cos ^{2} ( x )} : sec^{2} (x)

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

連鎖法則を適用:

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

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

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

= 2 sec (x) sec (x) tan (x)

簡素化

2 sec (x) sec (x) tan (x) : 2 sec^{2} (x) tan (x)

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