What is the solution for derivative of x^2+y^2=16 ?

The solution for derivative of x^2+y^2=16 is y=sqrt(16x+c_{1)-x^2},y=-sqrt(16x+c_{1)-x^2}

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derivative of x^2+y^2=16

\frac{d}{d x} (x^{2} + y^{2}) = 16

y = 16 x + c_{1} - x^{2}, y = - 16 x + c_{1} - x^{2}

Solution steps

\frac{d}{d x} (x^{2} + y^{2}) = 16

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

then

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

x^{2} + y^{2} = \int 16 d x

\int 16 d x = 16 x + c_{1}

x^{2} + y^{2} = 16 x + c_{1}

Isolate

y : y = 16 x + c_{1} - x^{2}, y = - 16 x + c_{1} - x^{2}

y = 16 x + c_{1} - x^{2}, y = - 16 x + c_{1} - x^{2}

\frac{d y}{d x} + 2 \cdot y = 0

\frac{d y}{e ^{y + 3}} = d t \cdot e^{t}

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

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

\frac{d x}{d t} = - \frac{x}{25}

What is the solution for derivative of x^2+y^2=16 ?
The solution for derivative of x^2+y^2=16 is y=sqrt(16x+c_{1)-x^2},y=-sqrt(16x+c_{1)-x^2}