(\partial)/(\partial x)(sqrt(p(q,x)q))

解

\frac{\partial}{\partial x} (p (q, x) q)

\frac{1}{2 p ( q , x ) q} pq (q, 1)

解答ステップ

\frac{\partial}{\partial x} (p (q, x) q)

p, q

を定数として扱う

連鎖法則を適用:

\frac{1}{2 p ( q , x ) q} \frac{\partial}{\partial x} (p (q, x) q)

= \frac{1}{2 p ( q , x ) q} \frac{\partial}{\partial x} (p (q, x) q)

\frac{\partial}{\partial x} (p (q, x) q) = pq (q, 1)

= \frac{1}{2 p ( q , x ) q} pq (q, 1)