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

解

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

6 x^{2} + y^{2}

解答ステップ

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

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

\frac{\partial}{\partial x} (2 x^{3}) = 6 x^{2}

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

= 6 x^{2} + y^{2}