derivative 30e^{x^2}x

解

導関数

30 e^{x^{2}} x

30 (2 e^{x^{2}} x^{2} + e^{x^{2}})

解答ステップ

\frac{d}{d x} (30 e^{x^{2}} x)

定数を除去:

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

= 30 \frac{d}{d x} (e^{x^{2}} x)

積の法則を適用:

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

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

= 30 (\frac{d}{d x} (e^{x^{2}}) x + \frac{d x}{d x} e^{x^{2}})

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

\frac{d x}{d x} = 1

= 30 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}})

簡素化

30 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}}) : 30 (2 e^{x^{2}} x^{2} + e^{x^{2}})

= 30 (2 e^{x^{2}} x^{2} + e^{x^{2}})