How to use the definition of a derivative to evaluate the limit

The video tutorial explains how to evaluate the derivative of a function at a specific point using the power rule. It begins by introducing the problem of finding F prime at C, where C equals 1/2. The function is identified using the limit definition, and the derivative is calculated. The tutorial then demonstrates the calculation of F prime at 1/2, highlighting a mistake in the process and correcting it.

What is the expression for F prime of 1/2 as calculated in the text?

What mistake does the speaker acknowledge regarding their calculations?