derivative of (4x^3-6(4x^2+4))

解

\frac{d}{d x} ((4 x^{3} - 6) (4 x^{2} + 4))

80 x^{4} + 48 x^{2} - 48 x

解答ステップ

\frac{d}{d x} ((4 x^{3} - 6) (4 x^{2} + 4))

積の法則を適用:

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

f = 4 x^{3} - 6, g = 4 x^{2} + 4

= \frac{d}{d x} (4 x^{3} - 6) (4 x^{2} + 4) + \frac{d}{d x} (4 x^{2} + 4) (4 x^{3} - 6)

\frac{d}{d x} (4 x^{3} - 6) = 12 x^{2}

\frac{d}{d x} (4 x^{2} + 4) = 8 x

= 12 x^{2} (4 x^{2} + 4) + 8 x (4 x^{3} - 6)

簡素化

12 x^{2} (4 x^{2} + 4) + 8 x (4 x^{3} - 6) : 80 x^{4} + 48 x^{2} - 48 x

= 80 x^{4} + 48 x^{2} - 48 x