(\partial)/(\partial x)(5x^2y^3+2x^2+7y)

解

\frac{\partial}{\partial x} (5 x^{2} y^{3} + 2 x^{2} + 7 y)

10 x y^{3} + 4 x

解答ステップ

\frac{\partial}{\partial x} (5 x^{2} y^{3} + 2 x^{2} + 7 y)

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} (5 x^{2} y^{3}) + \frac{\partial}{\partial x} (2 x^{2}) + \frac{\partial}{\partial x} (7 y)

\frac{\partial}{\partial x} (5 x^{2} y^{3}) = 10 y^{3} x

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

\frac{\partial}{\partial x} (7 y) = 0

= 10 y^{3} x + 4 x + 0

簡素化

= 10 x y^{3} + 4 x