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

解答

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

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

求解步骤

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

使用微分加减法定则:

(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)

化简

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)

d er i v a t i v e x (x^{2} + 4)^{0.5}

d er i v a t i v e \frac{1}{( x - 5 ) ^{2}}

\frac{d}{d t} (12 + 6 t)

d er i v a t i v e \frac{1}{a}

d er i v a t i v e \frac{x ^{2}}{p}