RD Sharma Solutions for Class 12 Maths Chapter 13 Derivative as a Rate Measurer

In mathematics, a rate is a ratio between two related quantities in different units. In describing the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate (for example a heart rate is expressed "beats per minute"). An essential application of derivatives is found in its use in calculating the rate of change of quantities for other quantities. You use such notions qualitatively every day without realizing them! For example, your mother intuitively knows that by how much amount should she add sugar to the tea to make it just the right amount of sweet.

If a quantity 'y' changes with a change in some other quantity 'x' given the fact that an equation of the form y = f(x) is always satisfied, i.e. 'y' is a function of 'x'; then the rate of change of 'y' for 'x' is given by




It's also sometimes known as the Average Rate of Change.

If the rate of change of a function is to be defined at a specific point, i.e. a particular value of 'x', it is known as the Instantaneous Rate of Change of the function at that point.