derivative of \sqrt[3]{cos(x})

解

\frac{d}{d x} (3 cos (x))

- \frac{sin ( x )}{3 cos ^{\frac{2}{3}} ( x )}

解答ステップ

\frac{d}{d x} (3 cos (x))

連鎖法則を適用:

\frac{1}{3 ( cos ( x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (cos (x))

= \frac{1}{3 ( cos ( x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (cos (x))

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

= \frac{1}{3 ( cos ( x ) ) ^{\frac{2}{3}}} (- sin (x))

簡素化

\frac{1}{3 cos ^{\frac{2}{3}} ( x )} (- sin (x)) : - \frac{sin ( x )}{3 cos ^{\frac{2}{3}} ( x )}

= - \frac{sin ( x )}{3 cos ^{\frac{2}{3}} ( x )}