(\partial)/(\partial y)(ln(3x^2-y^3-3))

Lösung

\frac{\partial}{\partial y} (ln (3 x^{2} - y^{3} - 3))

- \frac{3 y ^{2}}{3 x ^{2} - y ^{3} - 3}

Schritte zur Lösung

\frac{\partial}{\partial y} (ln (3 x^{2} - y^{3} - 3))

Behandle

x

als Konstante

Wende die Kettenregel an:

\frac{1}{3 x ^{2} - y ^{3} - 3} \frac{\partial}{\partial y} (3 x^{2} - y^{3} - 3)

= \frac{1}{3 x ^{2} - y ^{3} - 3} \frac{\partial}{\partial y} (3 x^{2} - y^{3} - 3)

\frac{\partial}{\partial y} (3 x^{2} - y^{3} - 3) = - 3 y^{2}

= \frac{1}{3 x ^{2} - y ^{3} - 3} (- 3 y^{2})

Vereinfache

\frac{1}{3 x ^{2} - y ^{3} - 3} (- 3 y^{2}) : - \frac{3 y ^{2}}{3 x ^{2} - y ^{3} - 3}

= - \frac{3 y ^{2}}{3 x ^{2} - y ^{3} - 3}

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