derivative f(x)=(x^2-5x+8)(3x^2-2)

解

導関数

f (x) = (x^{2} - 5 x + 8) (3 x^{2} - 2)

12 x^{3} - 45 x^{2} + 44 x + 10

解答ステップ

\frac{d}{d x} ((x^{2} - 5 x + 8) (3 x^{2} - 2))

積の法則を適用:

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

f = x^{2} - 5 x + 8, g = 3 x^{2} - 2

= \frac{d}{d x} (x^{2} - 5 x + 8) (3 x^{2} - 2) + \frac{d}{d x} (3 x^{2} - 2) (x^{2} - 5 x + 8)

\frac{d}{d x} (x^{2} - 5 x + 8) = 2 x - 5

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

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

簡素化

(2 x - 5) (3 x^{2} - 2) + 6 x (x^{2} - 5 x + 8) : 12 x^{3} - 45 x^{2} + 44 x + 10

= 12 x^{3} - 45 x^{2} + 44 x + 10