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

解

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

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

解答ステップ

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

\frac{\partial}{\partial x} (x^{9} y^{9}) = 9 y^{9} x^{8}

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

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