Exploring New Frontiers in Calculus: Logical Derivatives and Tangent Line Solutions

The basic problem of differential calculus is the problem of tangent lines and calculating the slope of the tangent line to the graph at a given point P and the less seemingly important problem of defining the vertical asymptote line and its derivative. The Logical Derivative makes it feasible to compute tangent line equations of vertical asymptote lines with the corresponding slope and direction of the asymptotes. L'hopitals indeterminate forms were used to evaluate Newton’s difference quotient and compute the logical derivative”. These are new derivatives developed using a method of direct proportions. By reversing the decrement and factoring it along with further analysis, derivatives derived are of the same dimension as their functions.