derivative of 4x^2cos(3x)

解答

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

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

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用微分乘法定则:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

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

化简

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

y^{^{''}} - 4 y^{^{'}} + 4 y = x e^{2 x}

\frac{d}{d x} ((1 + x + x^{2})^{99})

\frac{\partial}{\partial u} ((u^{2} + v^{2})^{\frac{3}{2}})

x \to 4 - lim (\frac{1}{x - 4})

\int (x^{2} - 1)^{- 1} d x