(\partial)/(\partial y)(x^3y^5+2x^4y)

解

\frac{\partial}{\partial y} (x^{3} y^{5} + 2 x^{4} y)

5 x^{3} y^{4} + 2 x^{4}

解答ステップ

\frac{\partial}{\partial y} (x^{3} y^{5} + 2 x^{4} y)

x

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 y} (x^{3} y^{5}) + \frac{\partial}{\partial y} (2 x^{4} y)

\frac{\partial}{\partial y} (x^{3} y^{5}) = 5 x^{3} y^{4}

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

= 5 x^{3} y^{4} + 2 x^{4}