(\partial)/(\partial p)(p^3q^2+2pq+p/q)

解

\frac{\partial}{\partial p} (p^{3} q^{2} + 2 pq + \frac{p}{q})

3 q^{2} p^{2} + 2 q + \frac{1}{q}

解答ステップ

\frac{\partial}{\partial p} (p^{3} q^{2} + 2 pq + \frac{p}{q})

q

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 p} (p^{3} q^{2}) + \frac{\partial}{\partial p} (2 pq) + \frac{\partial}{\partial p} (\frac{p}{q})

\frac{\partial}{\partial p} (p^{3} q^{2}) = 3 q^{2} p^{2}

\frac{\partial}{\partial p} (2 pq) = 2 q

\frac{\partial}{\partial p} (\frac{p}{q}) = \frac{1}{q}

= 3 q^{2} p^{2} + 2 q + \frac{1}{q}