What is (\partial)/(\partial p)(sqrt(pq)) ?

The answer to (\partial)/(\partial p)(sqrt(pq)) is (sqrt(q))/(2sqrt(p))

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(\partial)/(\partial p)(sqrt(pq))

\frac{\partial}{\partial p} (pq)

\frac{q}{2 p}

Solution steps

\frac{\partial}{\partial p} (pq)

Treat

q

as a constant

Apply the chain rule:

\frac{1}{2 pq} \frac{\partial}{\partial p} (pq)

= \frac{1}{2 pq} \frac{\partial}{\partial p} (pq)

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

= \frac{1}{2 pq} q

Simplify

\frac{1}{2 pq} q : \frac{q}{2 p}

= \frac{q}{2 p}

\frac{\partial}{\partial x} (3 + x ln (x y - 5))

\frac{\partial}{\partial x} (4 x^{3} + 4 y^{2} x + 4 x)

\int \frac{t}{t ^{4} + 2} d t

\frac{- 4 s + 8}{s ^{2} + 6 s + 8}

x \to \infty lim (7 - 2 x)

What is (\partial)/(\partial p)(sqrt(pq)) ?
The answer to (\partial)/(\partial p)(sqrt(pq)) is (sqrt(q))/(2sqrt(p))