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

解

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

10 x^{4} - 24 x^{3} + 12 x^{2} + 2 x - 3

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

(2 x - 3) (2 x^{3} + 1) + 6 x^{2} (x^{2} - 3 x + 2) : 10 x^{4} - 24 x^{3} + 12 x^{2} + 2 x - 3

= 10 x^{4} - 24 x^{3} + 12 x^{2} + 2 x - 3