derivative f(x)=x^2(-3x^2-2)

解

導関数

f (x) = x^{2} (- 3 x^{2} - 2)

- 12 x^{3} - 4 x

解答ステップ

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

積の法則を適用:

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

f = x^{2}, g = - 3 x^{2} - 2

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

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

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

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

簡素化

2 x (- 3 x^{2} - 2) + (- 6 x) x^{2} : - 12 x^{3} - 4 x

= - 12 x^{3} - 4 x