derivative of xe^xsin(2x)

解答

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

e^{x} sin (2 x) + x (e^{x} sin (2 x) + 2 e^{x} cos (2 x))

求解步骤

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

使用微分乘法定则:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{x} sin (2 x) + (e^{x} sin (2 x) + cos (2 x) \cdot 2 e^{x}) x

化简

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

\int (5 x^{4} + 3 x^{3} - 2) d x

\int (cos (θ) - 2 sin (θ))^{2} d θ

(x - y + 2) d x - (x - y) d y = 0

x \to 0 lim ((1 + 2 x)^{\frac{5}{x}})

t an g e n t 2 x^{3} + 2 x y + 2 y^{2} = 38, (- 1, - 4)