derivative of arctan(cos(x))

解

\frac{d}{d x} (arctan (cos (x)))

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

解答ステップ

\frac{d}{d x} (arctan (cos (x)))

連鎖法則を適用:

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

簡素化

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

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