What is the solution for derivative of y^2=8x ?

The solution for derivative of y^2=8x is y=sqrt(4x^2+c_{1)},y=-sqrt(4x^2+c_{1)}

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derivative of y^2=8x

\frac{d}{d x} (y^{2}) = 8 x

y = 4 x^{2} + c_{1}, y = - 4 x^{2} + c_{1}

Solution steps

\frac{d}{d x} (y^{2}) = 8 x

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

then

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

y^{2} = \int 8 x d x

\int 8 x d x = 4 x^{2} + c_{1}

y^{2} = 4 x^{2} + c_{1}

Isolate

y : y = 4 x^{2} + c_{1}, y = - 4 x^{2} + c_{1}

y = 4 x^{2} + c_{1}, y = - 4 x^{2} + c_{1}

What is the solution for derivative of y^2=8x ?
The solution for derivative of y^2=8x is y=sqrt(4x^2+c_{1)},y=-sqrt(4x^2+c_{1)}