This video explains how to find the gradient of a tangent to a curve using limits. An approximation for the gradient of the tangent is first discovered by drawing a secant on a curve, where two x co-ordinates are separated by value h. It then explains that as the value of h approaches, or tends to, zero, the approximation gets better and better until value h reaches zero where it is exact. It then uses the limit theory explained in the video, and applies it to find the derivative of a real function.