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

解

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

4 x - 3 y

解答ステップ

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

y, z

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

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

\frac{\partial}{\partial x} (3 x y) = 3 y

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

\frac{\partial}{\partial x} (4) = 0

= 4 x - 3 y + 0 - 0

簡素化

= 4 x - 3 y