d/(da)(sin^3(a)+cos^3(a))

解答

\frac{d}{d a} (sin^{3} (a) + cos^{3} (a))

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

求解步骤

\frac{d}{d a} (sin^{3} (a) + cos^{3} (a))

使用微分加减法定则:

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

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

\frac{d}{d a} (sin^{3} (a)) = 3 sin^{2} (a) cos (a)

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

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

t an g e n t f (x) = \frac{1}{5 + 2 x}, (2, \frac{1}{9})

f (x) = 3 x^{2} - 2

\int \frac{3 y ^{4} + 3 y ^{2} - 1}{y ^{3} + y} d y

\frac{d}{d y} (y (y - sin (x)))

x \to 10 lim (15)