(\partial)/(\partial y)(sqrt(41-x^2-4y^2))

Lösung

\frac{\partial}{\partial y} (41 - x^{2} - 4 y^{2})

- \frac{4 y}{41 - x ^{2} - 4 y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial y} (41 - x^{2} - 4 y^{2})

Behandle

x

als Konstante

Wende die Kettenregel an:

\frac{1}{2 41 - x ^{2} - 4 y ^{2}} \frac{\partial}{\partial y} (41 - x^{2} - 4 y^{2})

= \frac{1}{2 41 - x ^{2} - 4 y ^{2}} \frac{\partial}{\partial y} (41 - x^{2} - 4 y^{2})

\frac{\partial}{\partial y} (41 - x^{2} - 4 y^{2}) = - 8 y

= \frac{1}{2 41 - x ^{2} - 4 y ^{2}} (- 8 y)

Vereinfache

\frac{1}{2 41 - x ^{2} - 4 y ^{2}} (- 8 y) : - \frac{4 y}{41 - x ^{2} - 4 y ^{2}}

= - \frac{4 y}{41 - x ^{2} - 4 y ^{2}}

y^{^{''}} + \frac{y}{a} = 0

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d er i v a t i v e 6 t^{2} - t