(\partial)/(\partial x)(6x^7y^4+2x^6y^8)

解

\frac{\partial}{\partial x} (6 x^{7} y^{4} + 2 x^{6} y^{8})

42 y^{4} x^{6} + 12 y^{8} x^{5}

解答ステップ

\frac{\partial}{\partial x} (6 x^{7} y^{4} + 2 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} (6 x^{7} y^{4}) + \frac{\partial}{\partial x} (2 x^{6} y^{8})

\frac{\partial}{\partial x} (6 x^{7} y^{4}) = 42 y^{4} x^{6}

\frac{\partial}{\partial x} (2 x^{6} y^{8}) = 12 y^{8} x^{5}

= 42 y^{4} x^{6} + 12 y^{8} x^{5}