Introducing the derivative of the function ln x

Author:
joebridges
Graph shows the graph of ln x and a tangent to a point on the graph. The value of the point and value of the slope of the tangent are shown. The derivative of the function at the point is the value of the slope of the tangent at that point.
Move the point along the graph. What is the connection between the value of x for each point and the value of the slopes at each point? Remember in calculus that the derivative of the function is the slope function, so finding the slope gives the value of the derivative at that point.