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

解

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

x^{2}

解答ステップ

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

\frac{\partial}{\partial y} (x^{5}) = 0

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

\frac{\partial}{\partial y} (x) = 0

\frac{\partial}{\partial y} (2) = 0

= 0 + x^{2} + 0 + 0

簡素化

= x^{2}