(\partial)/(\partial x)(x^5+y^5-5x^3y^3)

解

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

5 x^{4} - 15 x^{2} y^{3}

解答ステップ

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

\frac{\partial}{\partial x} (x^{5}) = 5 x^{4}

\frac{\partial}{\partial x} (y^{5}) = 0

\frac{\partial}{\partial x} (5 x^{3} y^{3}) = 15 y^{3} x^{2}

= 5 x^{4} + 0 - 15 y^{3} x^{2}

簡素化

= 5 x^{4} - 15 x^{2} y^{3}