derivative 10(2e^{x^2}x^2+e^{x^2})

解

導関数

10 (2 e^{x^{2}} x^{2} + e^{x^{2}})

10 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

解答ステップ

\frac{d}{d x} (10 (2 e^{x^{2}} x^{2} + e^{x^{2}}))

定数を除去:

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

= 10 \frac{d}{d x} (2 e^{x^{2}} x^{2} + e^{x^{2}})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 10 (\frac{d}{d x} (2 e^{x^{2}} x^{2}) + \frac{d}{d x} (e^{x^{2}}))

\frac{d}{d x} (2 e^{x^{2}} x^{2}) = 2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x)

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

= 10 (2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x) + e^{x^{2}} \cdot 2 x)

拡張

2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x) + e^{x^{2}} \cdot 2 x : 4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x

= 10 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)