(\partial)/(\partial x)(5x^8y^5+2x^4y^6)

解

\frac{\partial}{\partial x} (5 x^{8} y^{5} + 2 x^{4} y^{6})

40 y^{5} x^{7} + 8 y^{6} x^{3}

解答ステップ

\frac{\partial}{\partial x} (5 x^{8} y^{5} + 2 x^{4} y^{6})

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} (5 x^{8} y^{5}) + \frac{\partial}{\partial x} (2 x^{4} y^{6})

\frac{\partial}{\partial x} (5 x^{8} y^{5}) = 40 y^{5} x^{7}

\frac{\partial}{\partial x} (2 x^{4} y^{6}) = 8 y^{6} x^{3}

= 40 y^{5} x^{7} + 8 y^{6} x^{3}