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

The answer to (\partial)/(\partial p)(p^3q^2+2pq+p/q) is 3q^2p^2+2q+1/q

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

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

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

Solution steps

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

Treat

q

as a constant

Apply the Sum/Difference Rule:

(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}

\int \frac{3 x ^{2}}{x ^{3} - 1} d x

f (x) = (ln (x^{5}))^{2}

\frac{d}{d x} (- \frac{1}{2} x cos (x))

\int \frac{9}{x ^{- 1} + 3} d x

\frac{\partial}{\partial x} (y cos (x^{2} y))

What is (\partial)/(\partial p)(p^3q^2+2pq+p/q) ?
The answer to (\partial)/(\partial p)(p^3q^2+2pq+p/q) is 3q^2p^2+2q+1/q