(\partial)/(\partial x)(6x^5y^6+8x^7y^8)

解

\frac{\partial}{\partial x} (6 x^{5} y^{6} + 8 x^{7} y^{8})

30 y^{6} x^{4} + 56 y^{8} x^{6}

解答ステップ

\frac{\partial}{\partial x} (6 x^{5} y^{6} + 8 x^{7} y^{8})

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} (6 x^{5} y^{6}) + \frac{\partial}{\partial x} (8 x^{7} y^{8})

\frac{\partial}{\partial x} (6 x^{5} y^{6}) = 30 y^{6} x^{4}

\frac{\partial}{\partial x} (8 x^{7} y^{8}) = 56 y^{8} x^{6}

= 30 y^{6} x^{4} + 56 y^{8} x^{6}