derivative f(x)=[(4x^2+3x)cos(x)]

解答

导数

f (x) = [(4 x^{2} + 3 x) cos (x)]

cos (x) (8 x + 3) - sin (x) (4 x^{2} + 3 x)

求解步骤

\frac{d}{d x} (((4 x^{2} + 3 x) cos (x)))

使用微分乘法定则:

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

f = 4 x^{2} + 3 x, g = cos (x)

= \frac{d}{d x} (4 x^{2} + 3 x) cos (x) + \frac{d}{d x} (cos (x)) (4 x^{2} + 3 x)

\frac{d}{d x} (4 x^{2} + 3 x) = 8 x + 3

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

= (8 x + 3) cos (x) + (- sin (x)) (4 x^{2} + 3 x)

化简

= cos (x) (8 x + 3) - sin (x) (4 x^{2} + 3 x)

\frac{\partial}{\partial x} (x^{2} - 4 x y + 3 y^{2})

\int_{0}^{2 π} e^{i x} d x

\int e^{x^{7}} d x

\int a r cot (x) d x

x \to 0 lim (\frac{( 5 ^{x} - 1 )}{x})