(x^3(8-3x))^'

解

(x^{3} (8 - 3 x))^{^{'}}

24 x^{2} - 12 x^{3}

解答ステップ

(x^{3} (8 - 3 x))^{'}

積の法則を適用:

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

f = x^{3}, g = 8 - 3 x

= (x^{3})^{^{'}} (8 - 3 x) + (8 - 3 x)^{^{'}} x^{3}

(x^{3})^{'} = 3 x^{2}

(8 - 3 x)^{'} = - 3

= 3 x^{2} (8 - 3 x) + (- 3) x^{3}

簡素化

3 x^{2} (8 - 3 x) + (- 3) x^{3} : 24 x^{2} - 12 x^{3}

= 24 x^{2} - 12 x^{3}