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

解

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

3 x^{2} + 1

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

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

= 3 x^{2} + 1