ABSTRACT
The chapter explains many methods and rules of differentiation. A good knowledge of algebra, in particular, laws of indices, is essential. Calculus is one of the most powerful mathematical tools used by engineers. The chapter presents how to differentiate common functions, products, quotients and function of a function. There are many practical situations engineers have to analyse which involve quantities that are varying. Typical examples include the stress in a loaded beam, the temperature of an industrial chemical, and the rate at which the speed of a vehicle is increasing or decreasing, the current in an electrical circuit or the torque on a turbine blade. Further examples include the voltage on a transmission line, the rate of growth of a bacteriological culture, and the rate at which the charge on a capacitor is changing. Differential calculus, or differentiation, is a mathematical technique for analysing the way in which functions change.
