(\partial)/(\partial x)(x^2+y^2(1-x)^3)

解

\frac{\partial}{\partial x} (x^{2} + y^{2} (1 - x)^{3})

2 x - 3 y^{2} (1 - x)^{2}

解答ステップ

\frac{\partial}{\partial x} (x^{2} + y^{2} (1 - x)^{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^{2}) + \frac{\partial}{\partial x} (y^{2} (1 - x)^{3})

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

\frac{\partial}{\partial x} (y^{2} (1 - x)^{3}) = - 3 y^{2} (1 - x)^{2}

= 2 x - 3 y^{2} (1 - x)^{2}