derivative f(x)=e^x(3x^2-6x+6)

解

導関数

f (x) = e^{x} (3 x^{2} - 6 x + 6)

3 e^{x} x^{2}

解答ステップ

\frac{d}{d x} (e^{x} (3 x^{2} - 6 x + 6))

積の法則を適用:

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

f = e^{x}, g = 3 x^{2} - 6 x + 6

= \frac{d}{d x} (e^{x}) (3 x^{2} - 6 x + 6) + \frac{d}{d x} (3 x^{2} - 6 x + 6) e^{x}

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

\frac{d}{d x} (3 x^{2} - 6 x + 6) = 6 x - 6

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

簡素化

e^{x} (3 x^{2} - 6 x + 6) + (6 x - 6) e^{x} : 3 e^{x} x^{2}

= 3 e^{x} x^{2}