derivative of 5e^xsin(x)

解

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

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

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

積の法則を適用:

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

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

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

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

\frac{d}{d x} (sin (x)) = cos (x)

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