(\partial)/(\partial x)(4x^2+xy+3y^2-8)

解

\frac{\partial}{\partial x} (4 x^{2} + x y + 3 y^{2} - 8)

8 x + y

解答ステップ

\frac{\partial}{\partial x} (4 x^{2} + x y + 3 y^{2} - 8)

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} (4 x^{2}) + \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (3 y^{2}) - \frac{\partial}{\partial x} (8)

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

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

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

\frac{\partial}{\partial x} (8) = 0

= 8 x + y + 0 - 0

簡素化

= 8 x + y