Problem: It is believed that Vedic Mathematics sutras are applicable for particular cases only in computation, whereas this study shows that the sutras have not been explored properly and if it is explored, a miracle may come out. Approach: In the present article we have analyzed the Vedic Mathematics Ekanyunena Purvena and Ekadhikena Purvena Sutras in finding the derivatives and antiderivatives of some elementary functions expressed in a power series using the power rule. We have also discussed the limitations of these sutras in finding derivative and antiderivative. For verification purpose, we have used Mathematica software to find the series of some functions, which can be applied for all elementary functions. Findings: Although it will be more laborious and time taking because to apply Vedic sutras, we have to follow four steps: to find series expansion, do term-wise operations, modify the new series to adjust it in some elementary functions and then write the result. In all examples, we start from Newton’s approach and end with Leibnitz’s approach to write the final result of derivative and antiderivative respectively. The study is strictly restricted to find the relevance of the Vedic sutras. Therefore three more formulae except sutras were added in the study to support their existence in modern mathematics especially in Calculus. Conclusion: Finally we have concluded that to study the derivative and antiderivative in total, three formulae for derivative and two formulae for antiderivative are sufficient i.e., using only these five formulae, we can study Calculus of single variable functions.