derivative of (x^3-2x^2+3(7x^2-4x))

解

\frac{d}{d x} ((x^{3} - 2 x^{2} + 3) (7 x^{2} - 4 x))

35 x^{4} - 72 x^{3} + 24 x^{2} + 42 x - 12

解答ステップ

\frac{d}{d x} ((x^{3} - 2 x^{2} + 3) (7 x^{2} - 4 x))

積の法則を適用:

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

f = x^{3} - 2 x^{2} + 3, g = 7 x^{2} - 4 x

= \frac{d}{d x} (x^{3} - 2 x^{2} + 3) (7 x^{2} - 4 x) + \frac{d}{d x} (7 x^{2} - 4 x) (x^{3} - 2 x^{2} + 3)

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

\frac{d}{d x} (7 x^{2} - 4 x) = 14 x - 4

= (3 x^{2} - 4 x) (7 x^{2} - 4 x) + (14 x - 4) (x^{3} - 2 x^{2} + 3)

簡素化

(3 x^{2} - 4 x) (7 x^{2} - 4 x) + (14 x - 4) (x^{3} - 2 x^{2} + 3) : 35 x^{4} - 72 x^{3} + 24 x^{2} + 42 x - 12

= 35 x^{4} - 72 x^{3} + 24 x^{2} + 42 x - 12