(\partial)/(\partial y)(sqrt(4-x^2-9y^2))

Lösung

\frac{\partial}{\partial y} (4 - x^{2} - 9 y^{2})

- \frac{9 y}{4 - x ^{2} - 9 y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial y} (4 - x^{2} - 9 y^{2})

Behandle

x

als Konstante

Wende die Kettenregel an:

\frac{1}{2 4 - x ^{2} - 9 y ^{2}} \frac{\partial}{\partial y} (4 - x^{2} - 9 y^{2})

= \frac{1}{2 4 - x ^{2} - 9 y ^{2}} \frac{\partial}{\partial y} (4 - x^{2} - 9 y^{2})

\frac{\partial}{\partial y} (4 - x^{2} - 9 y^{2}) = - 18 y

= \frac{1}{2 4 - x ^{2} - 9 y ^{2}} (- 18 y)

Vereinfache

\frac{1}{2 4 - x ^{2} - 9 y ^{2}} (- 18 y) : - \frac{9 y}{4 - x ^{2} - 9 y ^{2}}

= - \frac{9 y}{4 - x ^{2} - 9 y ^{2}}

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