What is the solution for derivative of x^2+(y^2/9)=1 ?

The solution for derivative of x^2+(y^2/9)=1 is y=3sqrt(x+c_{1)-x^2},y=-3sqrt(x+c_{1)-x^2}

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derivative of x^2+(y^2/9)=1

\frac{d}{d x} (x^{2} + \frac{y ^{2}}{9}) = 1

y = 3 x + c_{1} - x^{2}, y = - 3 x + c_{1} - x^{2}

Solution steps

\frac{d}{d x} (x^{2} + \frac{y ^{2}}{9}) = 1

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

then

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

x^{2} + \frac{y ^{2}}{9} = \int 1 d x

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

x^{2} + \frac{y ^{2}}{9} = x + c_{1}

Isolate

y : y = 3 x + c_{1} - x^{2}, y = - 3 x + c_{1} - x^{2}

y = 3 x + c_{1} - x^{2}, y = - 3 x + c_{1} - x^{2}

t^{\frac{3}{2}}

y = \frac{3}{2} x, y = 7 - x^{2}

\int \frac{t}{3 t ^{2} + 9} d t

y^{^{'}} = 8 y^{2}

\int t sec (t) tan (t) d t

What is the solution for derivative of x^2+(y^2/9)=1 ?
The solution for derivative of x^2+(y^2/9)=1 is y=3sqrt(x+c_{1)-x^2},y=-3sqrt(x+c_{1)-x^2}