How to Estimate a Derivative from a Graph

By Serm Murmson; Updated April 24, 2017
You can approximate the derivative of a graph using a tangent line.

A derivative is the instantaneous rate of change of a function. In other words, it is the slope of a function at a single point. If you have a graph, you can approximate its derivative at a point by calculating the slope of a tangent line at that point. Depending on the precision of your tangent line and the simplicity of your graph, your estimated derivative may be quite close to the actual derivative value.

Select the point of the graph at which you wish to estimate the derivative.

Draw a tangent line at that point using a ruler or straightedge. A tangent line is a line that touches the graph but does not intersect it at that point.

Select two points on your tangent line with clear x- and y-values.

Subtract the first x-value from the second.

Subtract the first y-value from the second.

Divide the difference in y-values by the difference in x-values. This is the slope of your tangent line, and is a good estimate of the derivative of your graph at the chosen point.

About the Author

Serm Murmson is a writer, thinker, musician and many other things. He has a bachelor's degree in anthropology from the University of Chicago. His concerns include such things as categories, language, descriptions, representation, criticism and labor. He has been writing professionally since 2008.