(\partial)/(\partial x)((x-2)(x^2+4))

解

\frac{\partial}{\partial x} ((x - 2) (x^{2} + 4))

3 x^{2} - 4 x + 4

解答ステップ

\frac{\partial}{\partial x} ((x - 2) (x^{2} + 4))

積の法則を適用:

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

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

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

\frac{\partial}{\partial x} (x - 2) = 1

\frac{\partial}{\partial x} (x^{2} + 4) = 2 x

= 1 \cdot (x^{2} + 4) + 2 x (x - 2)

簡素化

1 \cdot (x^{2} + 4) + 2 x (x - 2) : 3 x^{2} - 4 x + 4

= 3 x^{2} - 4 x + 4