(\partial)/(\partial x)(6y^2-4y^3-3x^2+6xy)

解

\frac{\partial}{\partial x} (6 y^{2} - 4 y^{3} - 3 x^{2} + 6 x y)

6 y - 6 x

解答ステップ

\frac{\partial}{\partial x} (6 y^{2} - 4 y^{3} - 3 x^{2} + 6 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} (6 y^{2}) - \frac{\partial}{\partial x} (4 y^{3}) - \frac{\partial}{\partial x} (3 x^{2}) + \frac{\partial}{\partial x} (6 x y)

\frac{\partial}{\partial x} (6 y^{2}) = 0

\frac{\partial}{\partial x} (4 y^{3}) = 0

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

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

= 0 - 0 - 6 x + 6 y

簡素化

= 6 y - 6 x