d/(da)(1+6cos^2(a)+cos^4(a))

解

\frac{d}{d a} (1 + 6 cos^{2} (a) + cos^{4} (a))

- 4 cos^{3} (a) sin (a) - 6 sin (2 a)

解答ステップ

\frac{d}{d a} (1 + 6 cos^{2} (a) + cos^{4} (a))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d a} (1) + \frac{d}{d a} (6 cos^{2} (a)) + \frac{d}{d a} (cos^{4} (a))

\frac{d}{d a} (1) = 0

\frac{d}{d a} (6 cos^{2} (a)) = - 12 cos (a) sin (a)

\frac{d}{d a} (cos^{4} (a)) = - 4 cos^{3} (a) sin (a)

= 0 - 12 cos (a) sin (a) - 4 cos^{3} (a) sin (a)

簡素化

0 - 12 cos (a) sin (a) - 4 cos^{3} (a) sin (a) : - 4 cos^{3} (a) sin (a) - 6 sin (2 a)

= - 4 cos^{3} (a) sin (a) - 6 sin (2 a)