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

解

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

\frac{y}{x} + y^{2}

解答ステップ

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

\frac{\partial}{\partial x} (y ln (x)) = \frac{y}{x}

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

= \frac{y}{x} + y^{2}