(\partial)/(\partial x)(xe^{2x}cos(3x))

解

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

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

解答ステップ

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

積の法則を適用:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

= 1 \cdot e^{2 x} cos (3 x) + (2 e^{2 x} cos (3 x) - 3 e^{2 x} sin (3 x)) x

簡素化

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