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Determine the rate of change of the circumference of a circle with respect to its radius.

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Lesson Parent:

Problem:

Answer:

$2\pi$

Solution:

Recall that the circumference of a circle has the formula

From this lesson we know that the rate of change of the circumference with respect to the radius is $C'(r)$ . Now we know that $C(r)$ is a polynomial function and that the derivative of a polynomial is known. Therefore,

Suppose that we have a circle of radius <Sign in to see all the formulas>. The circumference of the circle is

$C'(r)$ is a constant of

This is best said that the circumference of a circle will increase <Sign in to see all the formulas> per <Sign in to see all the formulas> increase in its radius.