derivative e^{6x}cos(9x)

解

導関数

e^{6 x} cos (9 x)

6 e^{6 x} cos (9 x) - 9 e^{6 x} sin (9 x)

解答ステップ

\frac{d}{d x} (e^{6 x} cos (9 x))

積の法則を適用:

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

f = e^{6 x}, g = cos (9 x)

= \frac{d}{d x} (e^{6 x}) cos (9 x) + \frac{d}{d x} (cos (9 x)) e^{6 x}

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

\frac{d}{d x} (cos (9 x)) = - sin (9 x) \cdot 9

= e^{6 x} \cdot 6 cos (9 x) + (- sin (9 x) \cdot 9) e^{6 x}

簡素化

= 6 e^{6 x} cos (9 x) - 9 e^{6 x} sin (9 x)