(\partial)/(\partial x)(x^7y^9-x^6y^8)

解

\frac{\partial}{\partial x} (x^{7} y^{9} - x^{6} y^{8})

7 y^{9} x^{6} - 6 y^{8} x^{5}

解答ステップ

\frac{\partial}{\partial x} (x^{7} y^{9} - x^{6} 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} (x^{7} y^{9}) - \frac{\partial}{\partial x} (x^{6} y^{8})

\frac{\partial}{\partial x} (x^{7} y^{9}) = 7 y^{9} x^{6}

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

= 7 y^{9} x^{6} - 6 y^{8} x^{5}