What is (\partial)/(\partial x)(sqrt(p(q,x)q)) ?

The answer to (\partial)/(\partial x)(sqrt(p(q,x)q)) is 1/(2sqrt(p(q,x)q))pq(q,1)

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

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

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

Solution steps

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

Treat

p, q

as a constant

Apply the chain rule:

\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)

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

\int \frac{1}{x} x^{'} d x

\frac{d}{d x} (sin (\frac{x}{1 + y}))

\frac{d}{d x} (5 π cos (π x))

\int_{- 2}^{3} \frac{38}{x ^{4}} d x

What is (\partial)/(\partial x)(sqrt(p(q,x)q)) ?
The answer to (\partial)/(\partial x)(sqrt(p(q,x)q)) is 1/(2sqrt(p(q,x)q))pq(q,1)