derivative of cos^2(x*sin(x))

解答

\frac{d}{d x} (cos^{2} (x) \cdot sin (x))

- 2 cos (x) + 3 cos^{3} (x)

求解步骤

\frac{d}{d x} (cos^{2} (x) sin (x))

使用微分乘法定则:

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

f = cos^{2} (x), g = sin (x)

= \frac{d}{d x} (cos^{2} (x)) sin (x) + \frac{d}{d x} (sin (x)) cos^{2} (x)

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

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

= (- sin (2 x)) sin (x) + cos (x) cos^{2} (x)

化简

(- sin (2 x)) sin (x) + cos (x) cos^{2} (x) : - 2 cos (x) + 3 cos^{3} (x)

= - 2 cos (x) + 3 cos^{3} (x)

\int_{0}^{4} 6 x d x

t an g e n t f (x) = x^{\frac{1}{2}}, (25, 5)

\frac{d}{d x} (lo g_{2} (3 2 x + 1))

\frac{d}{d x} (f (4 x^{5})) = 8 x^{4}

d er i v a t i v e cos (6 t)