derivative arctan(cos(θ))

解

導関数

arctan (cos (θ))

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

解答ステップ

\frac{d}{d θ} (arctan (cos (θ)))

連鎖法則を適用:

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

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

\frac{d}{d θ} (cos (θ)) = - sin (θ)

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

簡素化

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

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