In this video the speaker explains how to calculate limits and derivatives, specifically highlighting that the derivative of any constant is zero. The video reviews a list of common derivatives, including the power rule, exponential functions, logarithms, and trigonometric functions. The speaker also provides a proof for why the derivative of the natural logarithm is 1/x, using the definition of the exponential function and properties of logarithms. The goal is to help viewers memorize these derivatives and apply them easily in future math problems.