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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).
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