(\partial)/(\partial y)(tan(4+2x^2y^3z^2))

Lösung

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

sec^{2} (4 + 2 x^{2} y^{3} z^{2}) \cdot 6 x^{2} z^{2} y^{2}

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} (4 + 2 x^{2} y^{3} z^{2}) = 6 x^{2} z^{2} y^{2}

= sec^{2} (4 + 2 x^{2} y^{3} z^{2}) \cdot 6 x^{2} z^{2} y^{2}

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