(\partial)/(\partial x)(3+200x^2+300y^2)

解

\frac{\partial}{\partial x} (3 + 200 x^{2} + 300 y^{2})

400 x

解答ステップ

\frac{\partial}{\partial x} (3 + 200 x^{2} + 300 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} (3) + \frac{\partial}{\partial x} (200 x^{2}) + \frac{\partial}{\partial x} (300 y^{2})

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

\frac{\partial}{\partial x} (200 x^{2}) = 400 x

\frac{\partial}{\partial x} (300 y^{2}) = 0

= 0 + 400 x + 0

簡素化

= 400 x