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

Lösung

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

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

Schritte zur Lösung

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

Behandle

q, r

als Konstanten

Wende die Kettenregel an:

\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

Vereinfache

\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))

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d er i v a t i v e f (x) = 2 ln (6 + x)