derivative of x^5e^xcos(x)

解

\frac{d}{d x} (x^{5} e^{x} cos (x))

5 x^{4} e^{x} cos (x) + (e^{x} cos (x) - e^{x} sin (x)) x^{5}

解答ステップ

\frac{d}{d x} (x^{5} e^{x} cos (x))

積の法則を適用:

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

f = x^{5}, g = e^{x} cos (x)

= \frac{d}{d x} (x^{5}) e^{x} cos (x) + \frac{d}{d x} (e^{x} cos (x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (e^{x} cos (x)) = e^{x} cos (x) - e^{x} sin (x)

= 5 x^{4} e^{x} cos (x) + (e^{x} cos (x) - e^{x} sin (x)) x^{5}