derivative of-(cos^4(x)/4)

解

\frac{d}{d x} (- \frac{cos ^{4} ( x )}{4})

cos^{3} (x) sin (x)

解答ステップ

\frac{d}{d x} (- \frac{cos ^{4} ( x )}{4})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{4} \frac{d}{d x} (cos^{4} (x))

連鎖法則を適用:

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

= 4 (cos (x))^{3} \frac{d}{d x} (cos (x))

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

= - \frac{1}{4} \cdot 4 (cos (x))^{3} (- sin (x))

簡素化

- \frac{1}{4} \cdot 4 cos^{3} (x) (- sin (x)) : cos^{3} (x) sin (x)

= cos^{3} (x) sin (x)