(\partial)/(\partial z)(arctan(x^2yz^2))

Lösung

\frac{\partial}{\partial z} (arctan (x^{2} y z^{2}))

\frac{2 x ^{2} yz}{x ^{4} y ^{2} z ^{4} + 1}

Schritte zur Lösung

\frac{\partial}{\partial z} (arctan (x^{2} y z^{2}))

Behandle

x, y

als Konstanten

Wende die Kettenregel an:

\frac{1}{( x ^{2} y z ^{2} ) ^{2} + 1} \frac{\partial}{\partial z} (x^{2} y z^{2})

= \frac{1}{( x ^{2} y z ^{2} ) ^{2} + 1} \frac{\partial}{\partial z} (x^{2} y z^{2})

\frac{\partial}{\partial z} (x^{2} y z^{2}) = 2 x^{2} yz

= \frac{1}{( x ^{2} y z ^{2} ) ^{2} + 1} \cdot 2 x^{2} yz

Vereinfache

\frac{1}{( x ^{2} y z ^{2} ) ^{2} + 1} \cdot 2 x^{2} yz : \frac{2 x ^{2} yz}{x ^{4} y ^{2} z ^{4} + 1}

= \frac{2 x ^{2} yz}{x ^{4} y ^{2} z ^{4} + 1}