derivative of e^xcos(3x)

解

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

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

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

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