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

解

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

- 3 x^{2} + 10 x + 6

解答ステップ

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

積の法則を適用:

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

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

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

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

\frac{d}{d x} (6 - x) = - 1

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

簡素化

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

= - 3 x^{2} + 10 x + 6