(\partial)/(\partial x)((x^2+2)(x^3+1))

解

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

5 x^{4} + 6 x^{2} + 2 x

解答ステップ

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

積の法則を適用:

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

f = x^{2} + 2, g = x^{3} + 1

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

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

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

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

簡素化

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

= 5 x^{4} + 6 x^{2} + 2 x