(\partial)/(\partial x)(72y^7x^7-56y^6x^6)

解

\frac{\partial}{\partial x} (72 y^{7} x^{7} - 56 y^{6} x^{6})

504 y^{7} x^{6} - 336 y^{6} x^{5}

解答ステップ

\frac{\partial}{\partial x} (72 y^{7} x^{7} - 56 y^{6} x^{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} (72 y^{7} x^{7}) - \frac{\partial}{\partial x} (56 y^{6} x^{6})

\frac{\partial}{\partial x} (72 y^{7} x^{7}) = 504 y^{7} x^{6}

\frac{\partial}{\partial x} (56 y^{6} x^{6}) = 336 y^{6} x^{5}

= 504 y^{7} x^{6} - 336 y^{6} x^{5}