derivative of (e^{3x}(cos(2x)))

解答

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

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

求解步骤

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

使用微分乘法定则:

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

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

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

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

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

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

化简

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

16 y^{''} + 8 y^{'} + y = 0

x \to 0 lim (\frac{tan ( 4 x ) cos ( 6 x ) - tan ( 4 x )}{24 x ^{3}})

x \to + 1 lim (\frac{x - 1}{x ^{6} - 1})

x \to 0 lim (\frac{3 x}{sin ( 10 x )})

\frac{\partial}{\partial x} (3 (y - 1)^{3} (x - 6))