# Differentials to compute the maximum errors

Question: The radius of a circle was measured and found to be 10 cm with a possible error in measurement of +0.02 cm. Use differentials to compute the maximum error in using this radius to compute the area of the circle.

Okay, so I know that I have to find the derivative of the line so i can get my slope but Im not sure how to complete the rest of the problem. Please help!!

You have $$A=\pi r^2\implies \frac{dA}{dr}=2\pi r\implies dA=2\pi r\, dr\implies \Delta A=2\pi r\, \Delta r$$