(\partial)/(\partial x)(x^2+y^2+3xy+15x)

解

\frac{\partial}{\partial x} (x^{2} + y^{2} + 3 x y + 15 x)

2 x + 3 y + 15

解答ステップ

\frac{\partial}{\partial x} (x^{2} + y^{2} + 3 x y + 15 x)

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} (x^{2}) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (3 x y) + \frac{\partial}{\partial x} (15 x)

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

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

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

\frac{\partial}{\partial x} (15 x) = 15

= 2 x + 0 + 3 y + 15

簡素化

= 2 x + 3 y + 15