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

解

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

48 y^{7} x^{5} - 35 y^{6} x^{4}

解答ステップ

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

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

\frac{\partial}{\partial x} (8 x^{6} y^{7}) = 48 y^{7} x^{5}

\frac{\partial}{\partial x} (7 x^{5} y^{6}) = 35 y^{6} x^{4}

= 48 y^{7} x^{5} - 35 y^{6} x^{4}