(\partial)/(\partial x)(tan(9+2x^2y^4z^2))

Lösung

\frac{\partial}{\partial x} (tan (9 + 2 x^{2} y^{4} z^{2}))

sec^{2} (9 + 2 x^{2} y^{4} z^{2}) \cdot 4 y^{4} z^{2} x

Schritte zur Lösung

\frac{\partial}{\partial x} (tan (9 + 2 x^{2} y^{4} z^{2}))

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

sec^{2} (9 + 2 x^{2} y^{4} z^{2}) \frac{\partial}{\partial x} (9 + 2 x^{2} y^{4} z^{2})

= sec^{2} (9 + 2 x^{2} y^{4} z^{2}) \frac{\partial}{\partial x} (9 + 2 x^{2} y^{4} z^{2})

\frac{\partial}{\partial x} (9 + 2 x^{2} y^{4} z^{2}) = 4 y^{4} z^{2} x

= sec^{2} (9 + 2 x^{2} y^{4} z^{2}) \cdot 4 y^{4} z^{2} x

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