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

解

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

4 x^{3} - 2 x y

解答ステップ

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

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

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

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

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

= 4 x^{3} - 2 y x + 0

簡素化

= 4 x^{3} - 2 x y