Leibniz rule of calculus is to be found in most advanced texts in mathematics, such as Wylie and Barrett (1982) or Abramowitz and Stegun (1965). The rule is represented by the equation:
This rule is used in systems where integrations need to be performed over a time-dependent domain of integration. It provides a convenient transformation from the integral between transient limits of a temporal derivative to the temporal derivative of an integral between transient limits and vice versa.
Abramowitz, M. and Stegun, I. A. (1965) Handbook of Mathematical Functions. Dover, New York.
Majer, V. and Svoboda, V. (1985) Wylie, C. R. and Barrett, L. C. (1982) Advanced Engineering Mathematics. 5th Edn. McGraw-Hill Book Company.