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

解

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

4 x^{3} - 8 x y^{2}

解答ステップ

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

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

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

\frac{\partial}{\partial x} (y^{4}) = 0

\frac{\partial}{\partial x} (4 x^{2} y^{2}) = 8 y^{2} x

= 4 x^{3} + 0 - 8 y^{2} x

簡素化

= 4 x^{3} - 8 x y^{2}