derivative 0.08e^xx^2

解

導関数

0.08 e^{x} x^{2}

0.08 (e^{x} x^{2} + 2 x e^{x})

解答ステップ

\frac{d}{d x} (0.08 e^{x} x^{2})

定数を除去:

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

= 0.08 \frac{d}{d x} (e^{x} x^{2})

積の法則を適用:

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

f = e^{x}, g = x^{2}

= 0.08 (\frac{d}{d x} (e^{x}) x^{2} + \frac{d}{d x} (x^{2}) e^{x})

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

\frac{d}{d x} (x^{2}) = 2 x

= 0.08 (e^{x} x^{2} + 2 x e^{x})