d/(da)(cos(a)*sin(a))

解答

\frac{d}{d a} (cos (a) \cdot sin (a))

cos (2 a)

求解步骤

\frac{d}{d a} (cos (a) sin (a))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (a), g = sin (a)

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

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

\frac{d}{d a} (sin (a)) = cos (a)

= (- sin (a)) sin (a) + cos (a) cos (a)

化简

(- sin (a)) sin (a) + cos (a) cos (a) : cos (2 a)

= cos (2 a)

\int 6 sin^{2} (x co) s^{2} x d x

\frac{d}{d x} (\frac{6}{( x - 1 ) ^{2}})

t an g e n t f (x) = 6 cos (x) + 3 sin (2 x)

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = 2, y^{^{'}} (0) = 2

\frac{\partial}{\partial x} (1 + 3 x)