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

解

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

- 24 x^{5} + 96 x^{3} + 6 x^{2} - 12

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

(3 x^{2} - 6) (2 - 4 x^{3}) + (- 12 x^{2}) (x^{3} - 6 x) : - 24 x^{5} + 96 x^{3} + 6 x^{2} - 12

= - 24 x^{5} + 96 x^{3} + 6 x^{2} - 12