(\partial)/(\partial x)(ex^3-y^5)

解

\frac{\partial}{\partial x} (e x^{3} - y^{5})

3 e x^{2}

解答ステップ

\frac{\partial}{\partial x} (e x^{3} - y^{5})

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} (e x^{3}) - \frac{\partial}{\partial x} (y^{5})

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

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

= 3 e x^{2} - 0

簡素化

= 3 e x^{2}