derivative of (x^2-6(x^3+x^2+x+2))

解

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

5 x^{4} + 4 x^{3} - 15 x^{2} - 8 x - 6

解答ステップ

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

積の法則を適用:

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

f = x^{2} - 6, g = x^{3} + x^{2} + x + 2

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

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

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

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

簡素化

2 x (x^{3} + x^{2} + x + 2) + (3 x^{2} + 2 x + 1) (x^{2} - 6) : 5 x^{4} + 4 x^{3} - 15 x^{2} - 8 x - 6

= 5 x^{4} + 4 x^{3} - 15 x^{2} - 8 x - 6