(\partial)/(\partial y)(tan(1+2x^2y^4z^2))

Lösung

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

sec^{2} (1 + 2 x^{2} y^{4} z^{2}) \cdot 8 x^{2} z^{2} y^{3}

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} (1 + 2 x^{2} y^{4} z^{2}) = 8 x^{2} z^{2} y^{3}

= sec^{2} (1 + 2 x^{2} y^{4} z^{2}) \cdot 8 x^{2} z^{2} y^{3}

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