# RD Sharma Class 12 Chapter 13 Solutions (Derivative As A Rate Measurer)

RD Sharma Class 12 Maths Solutions Chapter 13 Derivative as a Rate Measurer helps you to learn the most basic to advanced concepts of this chapter. Solving these problems will help you to learn more about the type of questions you can expect in CBSE Class 12 Board exams as well as engineering entrance exams. The topics that will be discussed in Chapter 13 Derivative as a Rate Measurer are derivative as a rate measurer and related rates.

The RD Sharma Class 12 Solutions Maths Chapter 13 Derivative as a Rate Measurer is divided into two exercises and 41 questions. The purpose of these exercises is to teach you the basics of the concept and help you answer these questions from CBSE and entrance exams with more confidence and ease. You will see the questions are arranged in exactly the same arrangement as provided in the RD Sharma Class 12 Maths Solutions for Derivative As A Rate Measurer.

If you practice problems given in RD Sharma Class 12 Maths Solutions Chapter 13 Derivative as a Rate Measurer, you are only strengthening your base for Board exams ahead. Instasolv can help you get good grades that you will need to be eligible for entrance examinations. On practising these solutions a number of times, you can also solve different problems of various difficulty levels and apply your logic and understanding of the chapter.

## Topics Covered in RD Sharma Class 12 Maths Solutions Chapter 13 Derivative as a Rate Measurer

**Derivative as a Rate Measurer**

When y = f(x), a function of x and Δy is the change in the function corresponding to Δx, a small change in x. Then Δy/Δx can be represented as a change in the function y due to a small change in x.

Putting this in detail, you can say Δy/Δx would be the average rate of change in y w.r.t a unit change in x. This means x has changed to x + Δx.

Now when Δx -> 0, the limiting value of function y’s average rate of change w.r.t x in the given interval [x, x+Δx] is known as y’s instantaneous rate of change w.r.t x.

Therefore,

Lim Δx -> 0 (Δy/Δx) becomes y’s instantaneous rate of change w.r.t x

=> dy/dx can be deduced the rate of change in y w.r.t x.

You can choose not to use the term “instantaneous”.

Hence, considering the above discussion it would be safe to say that dy/dx is y’s rate of change w.r.t x for a specific value of x.

**Note – **(dy/dx)x =x_{0} I.e. dy/dx at x = x_{0} is the rate of change in y w.r.t x, given x=x_{0}.

**Note – **if x = Φ(t) and y = Ψ(t), then dy/dx = (dy/dx)/(dx/dt), given dx/dt ≠ 0.

Therefore, the rate of change in y w.r.t x is the rate of change in y and x w.r.t ‘t’.

Please consider the rate of change as an instantaneous rate of change.

**Related Rates**

The instantaneous rate of change in one quantity requires corresponding to the rate of change in another quantity. We can exemplify this by taking a volume of a spherical balloon. Suppose the instantaneous rate of change in its volume is needed when its radius is available. So in such problems, we need to deduce a relation that connects and differentiates them w.r.t time.

### Discussion of Exercises of RD Sharma Class 12 Maths Chapter 13 Derivative as a Rate Measurer

- The chapter has two exercises for you to solve different types of questions you might get in your CBSE and entrance exams. The first exercise will ask you to find the rate of change of total surface area or a volume of an object of a specific shape. The inputs you will have could be the height, radius, diameter, etc. These problems will help you to answer questions that are based on the concept of the chapter.
- The second exercise has 31 questions where you will be asked to find the instantaneous rate of change in a given shape with specific measurements.

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