(\partial)/(\partial x)(yx^3-xy^2+xy+13y)

解

\frac{\partial}{\partial x} (y x^{3} - x y^{2} + x y + 13 y)

- y^{2} + 3 y x^{2} + y

解答ステップ

\frac{\partial}{\partial x} (y x^{3} - x y^{2} + x y + 13 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} (y x^{3}) - \frac{\partial}{\partial x} (x y^{2}) + \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (13 y)

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

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

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

\frac{\partial}{\partial x} (13 y) = 0

= 3 y x^{2} - y^{2} + y + 0

簡素化

= - y^{2} + 3 y x^{2} + y