derivative of sqrt(1+cos^2(x))

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

= \frac{1}{2 1 + cos ^{2} ( x )} (- sin (2 x))

簡素化

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

= - \frac{sin ( 2 x )}{2 1 + cos ^{2} ( x )}