derivative of (2x^4-1(5x^3+6x))

解

\frac{d}{d x} ((2 x^{4} - 1) (5 x^{3} + 6 x))

70 x^{6} + 60 x^{4} - 15 x^{2} - 6

解答ステップ

\frac{d}{d x} ((2 x^{4} - 1) (5 x^{3} + 6 x))

積の法則を適用:

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

f = 2 x^{4} - 1, g = 5 x^{3} + 6 x

= \frac{d}{d x} (2 x^{4} - 1) (5 x^{3} + 6 x) + \frac{d}{d x} (5 x^{3} + 6 x) (2 x^{4} - 1)

\frac{d}{d x} (2 x^{4} - 1) = 8 x^{3}

\frac{d}{d x} (5 x^{3} + 6 x) = 15 x^{2} + 6

= 8 x^{3} (5 x^{3} + 6 x) + (15 x^{2} + 6) (2 x^{4} - 1)

簡素化

8 x^{3} (5 x^{3} + 6 x) + (15 x^{2} + 6) (2 x^{4} - 1) : 70 x^{6} + 60 x^{4} - 15 x^{2} - 6

= 70 x^{6} + 60 x^{4} - 15 x^{2} - 6