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

解

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

4 (3 x^{2} + y^{2}) - 4 a^{2}

解答ステップ

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

a, y

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (4 x (x^{2} + y^{2})) = 4 (3 x^{2} + y^{2})

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

= 4 (3 x^{2} + y^{2}) - 4 a^{2}