(\partial)/(\partial x)(42y^8x^5-30y^7x^4)

解

\frac{\partial}{\partial x} (42 y^{8} x^{5} - 30 y^{7} x^{4})

210 y^{8} x^{4} - 120 y^{7} x^{3}

解答ステップ

\frac{\partial}{\partial x} (42 y^{8} x^{5} - 30 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} (42 y^{8} x^{5}) - \frac{\partial}{\partial x} (30 y^{7} x^{4})

\frac{\partial}{\partial x} (42 y^{8} x^{5}) = 210 y^{8} x^{4}

\frac{\partial}{\partial x} (30 y^{7} x^{4}) = 120 y^{7} x^{3}

= 210 y^{8} x^{4} - 120 y^{7} x^{3}