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

解

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

2 x - 4

解答ステップ

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

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

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

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

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

\frac{\partial}{\partial x} (3) = 0

= 0 + 2 x - 4 - 0

簡素化

= 2 x - 4