(\partial)/(\partial z)(tan(1+2x^2y^3z^2))

Lösung

\frac{\partial}{\partial z} (tan (1 + 2 x^{2} y^{3} z^{2}))

sec^{2} (1 + 2 x^{2} y^{3} z^{2}) \cdot 4 x^{2} y^{3} z

Schritte zur Lösung

\frac{\partial}{\partial z} (tan (1 + 2 x^{2} y^{3} z^{2}))

Behandle

x, y

als Konstanten

Wende die Kettenregel an:

sec^{2} (1 + 2 x^{2} y^{3} z^{2}) \frac{\partial}{\partial z} (1 + 2 x^{2} y^{3} z^{2})

= sec^{2} (1 + 2 x^{2} y^{3} z^{2}) \frac{\partial}{\partial z} (1 + 2 x^{2} y^{3} z^{2})

\frac{\partial}{\partial z} (1 + 2 x^{2} y^{3} z^{2}) = 4 x^{2} y^{3} z

= sec^{2} (1 + 2 x^{2} y^{3} z^{2}) \cdot 4 x^{2} y^{3} z

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