to the explanation of the course of Nature.” — WHITEHEAD v . Introduction In Chapter , we have learnt how to find derivative of composite functions, inverse trigonometric functions, implicit functions, exponential functions and logarithmic functions. In this chapter, we will study applications of the derivative in various disciplines, e.g., in engineering, science, social science, and many other fields. For instance, we will learn how the derivative can be used (i) to determine rate of change of quantities, (ii) to find the equations of tangent and normal to a curve at a point, (iii) to find turning points on the graph of a function which in turn will help us to locate points at which largest or smallest value (locally) of a function occurs.
We will also use derivative to find intervals on which a function is increasing or decreasing. Finally, we use the derivative to find approximate value of certain quantities. . Rate of Change of Quantities Recall that by the derivative ds dt , we mean the rate of change of distance s with respect to the time t .
In a similar fashion, whenever one quantity y varies with another quantity x , satisfying some rule y f x , then dy dx (or f ′ ( x )) represents the rate of change of y with respect to x and dy dx x x = (or f ′ ( x )) represents the rate of change of y with respect to x at Further, if two variables x and y are varying with respect to another variable t , i.e., if f t and y g t , then by Chain Rule dy dx = dy dx dt , if dx dt ≠