(\partial)/(\partial x)(x^8+5xy^9)

解

\frac{\partial}{\partial x} (x^{8} + 5 x y^{9})

8 x^{7} + 5 y^{9}

解答ステップ

\frac{\partial}{\partial x} (x^{8} + 5 x 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} (x^{8}) + \frac{\partial}{\partial x} (5 x y^{9})

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

\frac{\partial}{\partial x} (5 x y^{9}) = 5 y^{9}

= 8 x^{7} + 5 y^{9}