derivative of sqrt(cos(x+1))

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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