(\partial)/(\partial x)(7y^9+5y^7x^4)

解

\frac{\partial}{\partial x} (7 y^{9} + 5 y^{7} x^{4})

20 y^{7} x^{3}

解答ステップ

\frac{\partial}{\partial x} (7 y^{9} + 5 y^{7} x^{4})

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} (7 y^{9}) + \frac{\partial}{\partial x} (5 y^{7} x^{4})

\frac{\partial}{\partial x} (7 y^{9}) = 0

\frac{\partial}{\partial x} (5 y^{7} x^{4}) = 20 y^{7} x^{3}

= 0 + 20 y^{7} x^{3}

簡素化

= 20 y^{7} x^{3}