derivative of 1/(sqrt(1-sin^2(x)))

解

\frac{d}{d x} \frac{1}{1 - sin ^{2} ( x )}

sec (x) tan (x)

解答ステップ

\frac{d}{d x} \frac{1}{1 - sin ^{2} ( x )}

簡素化

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

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

連鎖法則を適用:

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

= \frac{1}{2 sec ^{2} ( x )} \frac{d}{d x} (sec^{2} (x))

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

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

簡素化

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

= sec (x) tan (x)