Abstract
<jats:p>Calculus is based on an understanding of the graphical depiction of the derivatives and its functions which remain important in mathematics, yet there are many misconceptions which could impede a student's advancement in these topics. On this note, the idea that the slope of the line passing through a point represents the derivative of a function at that point is a common fallacy. Because this idea ignores the believe that the tangent line is the limit of secant lines as they approach the point of tangency. Therefore, the ideas of the derivatives and their uses were seen in an overly simplistic light. These misinterpreting of the derivative as a ratio of dy to dx instead of seeing it as the average rate of change's limit is another prevailing misunderstanding among the students. Due to this misperception, differentiation was approached mechanically without consideration for its theoretical foundations among the students. As a result of this, some students find it difficult and often misuse it, misidentifying the inner and outer functions and failing to recognize the composition of functions. And this had led to certain misunderstandings and misconceptions when it came to applying the graphical method for computing derivatives in mathematics. The result of this study had led to recognizing some misconceptions, including incorrect assumptions made when learning new concepts, and this include, conceptual misconceptions, conceptual errors, generalization or transfer errors, ignorance of rule restrictions, and insufficient application of rules. A qualitative method was used for the study with the selection of Grade 12 math students from a South African high school to accomplish the study's goal.</jats:p>