(\partial)/(\partial x)(x^6+xy^5+7)

解

\frac{\partial}{\partial x} (x^{6} + x y^{5} + 7)

6 x^{5} + y^{5}

解答ステップ

\frac{\partial}{\partial x} (x^{6} + x y^{5} + 7)

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^{6}) + \frac{\partial}{\partial x} (x y^{5}) + \frac{\partial}{\partial x} (7)

\frac{\partial}{\partial x} (x^{6}) = 6 x^{5}

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

\frac{\partial}{\partial x} (7) = 0

= 6 x^{5} + y^{5} + 0

簡素化

= 6 x^{5} + y^{5}