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

解

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

40 x^{3} - 39 x^{2} + 8 x + 5

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} (5 x - 4) = 5

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

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

簡素化

5 (2 x^{3} - x^{2} + 1) + (6 x^{2} - 2 x) (5 x - 4) : 40 x^{3} - 39 x^{2} + 8 x + 5

= 40 x^{3} - 39 x^{2} + 8 x + 5