Chapter 2 Differentiation 2nd Year Mathematics

The ancient Greeks possessed knowledge of concepts such as area, volume, and centroids, which are linked to integral calculus. Subsequently, in the seventeenth century, Sir Isaac Newton, an English mathematician (1642-1727), and Gottfried Wilhelm Leibniz, a German mathematician (1646-1716), independently tackled the problem of instantaneous rates of change, leading to the invention of differential calculus. Following the development of calculus, mathematics emerged as a potent tool for addressing rates of change and describing the physical universe.

Differential calculus primarily concerns itself with the rate of change of a dependent variable concerning one or more independent variables. To understand this better, let’s delve into the terms “dependent” and “independent” variables.

Exercise 2.1

Exercise 2.2

Exercise 2.3

Exercise 2.4

Exercise 2.5

Exercise 2.6

Exercise 2.7

Exercise 2.8

Exercise 2.9

Exercise 2.10

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