What are the derivatives of circle?

The derivative at a given point in a circle is the tangent to

the circle at that point.

To find the derivative of a circle you must use implicit differentiation.

The equation of a circle:

x^2 + y^2 = r^2

Take the derivative of both sides. Since r is always a constant, it does not matter what it is. The derivative of a constant is always zero, so the value of r will not affect the final answer for the derivative of a circle.

2x + 2y * dy/dx = 0

2y * dy/dx = -2x

dy/dx = -2x/2y

Simplify:

dy/dx = -(x/y)

The derivative of a circle of any radius at any point on that circle is -(x/y).