Calculation of Two Types of Quaternion Step Derivatives of Elementary Functions

We aim to get the step derivative of a complex function, as it derives in imaginary direction real function. Given that function cannot be derived using i, which is used derive we intend base quaternion. Because many analytical studies on quaternions have been conducted, various examples can presented expression elementary In previous study, quaternion was regarded separate from basis number. However, considering properties quaternion, propose two types derivatives this study. The first defined j direction, includes Furthermore, j+k2 determined rule between bases j, and k present definition j-step (j,k)-step are applied functions ez, sinz, cosz.