A new approach for executing differential calculus and application to failure rate analysis

We propose a new approach to executing differential calculus using simple 2 by 2 matrices and demonstrate an important application to the reliability engineering field. This matrix approach prevents an exponential increase in computation time of the post-expression obtained by differential calculus and shows instead a linear increase. This approach is a breakthrough for solving computation problems not only in the reliability engineering field but also in almost all science and engineering fields because differential calculus is essential to and commonly used in almost all of them.