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

解

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

3 x^{2} + y^{2}

解答ステップ

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

y

を定数として扱う

積の法則を適用:

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

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

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

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

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

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

簡素化

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

= 3 x^{2} + y^{2}