(\partial)/(\partial x)(2x^3+3y^2-6xy+2)

解

\frac{\partial}{\partial x} (2 x^{3} + 3 y^{2} - 6 x y + 2)

6 x^{2} - 6 y

解答ステップ

\frac{\partial}{\partial x} (2 x^{3} + 3 y^{2} - 6 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} (2 x^{3}) + \frac{\partial}{\partial x} (3 y^{2}) - \frac{\partial}{\partial x} (6 x y) + \frac{\partial}{\partial x} (2)

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

\frac{\partial}{\partial x} (6 x y) = 6 y

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

= 6 x^{2} + 0 - 6 y + 0

簡素化

= 6 x^{2} - 6 y