What is (\partial)/(\partial p)(arctan(pqr)) ?

The answer to (\partial)/(\partial p)(arctan(pqr)) is (qr)/(p^2q^2r^2+1)

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(\partial)/(\partial p)(arctan(pqr))

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

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

Solution steps

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

Treat

q, r

as constants

Apply the chain rule:

\frac{1}{( pq r ) ^{2} + 1} \frac{\partial}{\partial p} (pq r)

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

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

= \frac{1}{( pq r ) ^{2} + 1} q r

Simplify

\frac{1}{( pq r ) ^{2} + 1} q r : \frac{q r}{p ^{2} q ^{2} r ^{2} + 1}

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

- cot (x) = \frac{v ^{'}}{v ^{2}}

\int tan^{4} (11 x) d x

\frac{\partial}{\partial z} (4 sin^{2} (z))

\int (x - \frac{1}{x}) d x

\frac{d}{d x} (e^{2^{x}})

What is (\partial)/(\partial p)(arctan(pqr)) ?
The answer to (\partial)/(\partial p)(arctan(pqr)) is (qr)/(p^2q^2r^2+1)