derivative (x^3-5x)(4x^2-3x)

解

導関数

(x^{3} - 5 x) (4 x^{2} - 3 x)

20 x^{4} - 12 x^{3} - 60 x^{2} + 30 x

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

(3 x^{2} - 5) (4 x^{2} - 3 x) + (8 x - 3) (x^{3} - 5 x) : 20 x^{4} - 12 x^{3} - 60 x^{2} + 30 x

= 20 x^{4} - 12 x^{3} - 60 x^{2} + 30 x