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

解

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

8 x^{3} + y

解答ステップ

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

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

\frac{\partial}{\partial x} (2 x^{4}) = 8 x^{3}

\frac{\partial}{\partial x} (5 y^{2}) = 0

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

= 8 x^{3} + 0 + y

簡素化

= 8 x^{3} + y