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人気のある微分積分 >

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

解

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

解

4 y x + 3 y^{2}

解答ステップ

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

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

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

= 4 y x + 3 y^{2}

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