derivative of (x^2/(64)+(y^2)/(25))=1

Lösung

\frac{d}{d x} (\frac{x ^{2}}{64} + \frac{y ^{2}}{25}) = 1

y = \frac{5 64 x + c _{1} - x ^{2}}{8}, y = - \frac{5 64 x + c _{1} - x ^{2}}{8}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{64} + \frac{y ^{2}}{25}) = 1

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

\frac{x ^{2}}{64} + \frac{y ^{2}}{25} = \int 1 d x

\int 1 d x = x + c_{1}

\frac{x ^{2}}{64} + \frac{y ^{2}}{25} = x + c_{1}

Isoliere

y : y = \frac{5 64 x + 64 c _{1} - x ^{2}}{8}, y = - \frac{5 64 x + 64 c _{1} - x ^{2}}{8}

y = \frac{5 64 x + 64 c _{1} - x ^{2}}{8}, y = - \frac{5 64 x + 64 c _{1} - x ^{2}}{8}

Vereinfache

y = \frac{5 64 x + c _{1} - x ^{2}}{8}, y = - \frac{5 64 x + c _{1} - x ^{2}}{8}

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