(\partial)/(\partial x)(2xy^7+x^7y^9)

解

\frac{\partial}{\partial x} (2 x y^{7} + x^{7} y^{9})

2 y^{7} + 7 y^{9} x^{6}

解答ステップ

\frac{\partial}{\partial x} (2 x y^{7} + x^{7} y^{9})

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} (2 x y^{7}) + \frac{\partial}{\partial x} (x^{7} y^{9})

\frac{\partial}{\partial x} (2 x y^{7}) = 2 y^{7}

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

= 2 y^{7} + 7 y^{9} x^{6}