derivative of e^x(13x^2-26x+26)

解

\frac{d}{d x} (e^{x} (13 x^{2} - 26 x + 26))

13 e^{x} x^{2}

解答ステップ

\frac{d}{d x} (e^{x} (13 x^{2} - 26 x + 26))

積の法則を適用:

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

f = e^{x}, g = 13 x^{2} - 26 x + 26

= \frac{d}{d x} (e^{x}) (13 x^{2} - 26 x + 26) + \frac{d}{d x} (13 x^{2} - 26 x + 26) e^{x}

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

\frac{d}{d x} (13 x^{2} - 26 x + 26) = 26 x - 26

= e^{x} (13 x^{2} - 26 x + 26) + (26 x - 26) e^{x}

簡素化

e^{x} (13 x^{2} - 26 x + 26) + (26 x - 26) e^{x} : 13 e^{x} x^{2}

= 13 e^{x} x^{2}