(\partial)/(\partial x)(x^3+y^5+x^7-y^2)

解

\frac{\partial}{\partial x} (x^{3} + y^{5} + x^{7} - y^{2})

7 x^{6} + 3 x^{2}

解答ステップ

\frac{\partial}{\partial x} (x^{3} + y^{5} + x^{7} - y^{2})

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^{3}) + \frac{\partial}{\partial x} (y^{5}) + \frac{\partial}{\partial x} (x^{7}) - \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

\frac{\partial}{\partial x} (y^{5}) = 0

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

\frac{\partial}{\partial x} (y^{2}) = 0

= 3 x^{2} + 0 + 7 x^{6} - 0

簡素化

= 7 x^{6} + 3 x^{2}