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

解

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

x^{4} - 6 x^{5} y

解答ステップ

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

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

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

\frac{\partial}{\partial y} (3 x^{5} y^{2}) = 6 x^{5} y

= x^{4} - 6 x^{5} y