Circle Secrets Revealed: Using Infinitesimals to Find the Derivative of Area #shorts

Have you ever wondered why the derivative of the area formula for a circle is equal to the formula for its circumference? Let the tip of your pen represent an infinitesimal length dr, and increase the radius of the circle by dr. The corresponding change in area, dA, is equal to the circumference of the circle times the infinitesimal length, dr. Dividing both sides of this equation by dr shows that the derivative of area with respect to radius is equal to the circumference of the circle.