Background/purpose. One of the current problems facing mathematics students, graduates in mathematics, and engineering is the disconnection between the meanings, symbolic representations, and graphics of derivatives when solving problems, which hinders their understanding. This article analyzes engineering students' understanding activated by connections made to solve tasks on derivatives in a graphical context. To do so, networking between the Extended Theory of Connections and the Onto-semiotic Approach will be used. Materials/methods. The methodology was qualitative and exploratory. A questionnaire was designed with three tasks on the meaning of the derivative and the graphs of the function f and the derivative f'. This questionnaire was administered in the context of participant observation to nineteen engineering students who volunteered. The collected and video-recorded data were analyzed using the theoretical tool from an onto-semiotic view. Results. The results show that students who have a level 2 understanding of the derivative (graphically) because they sketch the graph of f' given the graph of f and sketch the graph of f from the graph of f', establishing mathematical connections of implication, different representations, meaning, procedural, part-whole and the main connection of reversibility that allowed them to make the two graphs. Students who have level 1 understanding establish consistent connections, but do not argue or have details to correct in the graphs. Conclusion. Other students have level 0 understanding because they did not make the graphs of f and f' because they did not activate mathematical connections but personal connections, assuming that the graph of the derivative is a reflection of the graph of the original function, they do not locate the relative extremes, inflection points, monotony due to poor conceptual understanding.