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

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Last updated date: 28th May 2024
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RD Sharma Solutions for Class 12 Maths Chapter 13 - Derivative as a Rate Measurer - Free PDF Downlaod

Derivative as a Rate Measure is an important chapter in class 12 Maths. The concepts developed from this chapter help in problems of physics also. Studying and practicing from RD Sharma is a good option for growing concepts and confidence in this chapter. In the previous chapter, we have learned about the computation of derivatives. This chapter will learn applications of derivatives as a rate measure. Students can access RD Sharma Class 12 Derivative as a Rate Measurer from the below provided links. This chapter is mainly focused on the instantaneous rate of change of a given physical quantity.

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Competitive Exams after 12th Science

Class 12 RD Sharma Textbook Solutions Chapter 13 - Derivative as a Rate Measurer

Some of the Essential Topics Which Are Discussed in This Chapter Are Listed Below

  • Definition of derivative as a rate measurer.

  • Meaning of derivative as a rate measurer.

  • Theorems and applications on derivative as a rate measurer.

  • Definition and meaning of related rates.

RD Sharma Solutions provided here in this pdf are in a detailed approach, which helps students to get good marks and makes the exam preparation effective for them. Also, practice is an essential task to learn and score well in Mathematics. Hence, we Vedantu have provided solutions to the ample number of questions that are present in RD Sharma Books. The solution provided in this pdf can give a good boost to the students to perform very well in their board exams.


Introduction to Derivative As Rate Measure

If a quantity y depends and varies with a quantity x, then the rate of change of y with respect to x is denoted by dy/dx. For example, the rate of change of pressure p with respect to height h denoted by dp/dh.

A rate of change with respect to time is simply called the rate of change. A rate of change of current is denoted by di/dt and a rate of change of temperature θ is denoted by dθ/dt.


Exercises in RD Sharma Solutions For Class 12 Maths Chapter 13 PDF


Applications of Derivative as a Rate Measure

  • It is used to determine a new value of a quantity from the old value and the amount of change.

  • It helps us to calculate the average rate of change and explains how it differs from the instantaneous rate of change.

  • We can apply rates of change to displacement, velocity, and acceleration of an object moving along a straight line.

  • It is also used to predict the future population from the present value and the population growth rate.

  • Derivatives are used to calculate marginal cost and revenue in a business situation.


Conclusion

These solutions are formulated by Vedantu experts in an interactive manner to create interest in learning among students. Solutions provided by RD Sharma also contain explanatory diagrams and tables for comparative study, which makes it easy to learn the crucial topics. Students who find difficulty in solving these topics are suggested to go through solutions provided by RD Sharma. These solutions are prepared from the exam point of view and according to the latest syllabus. 


FAQs on RD Sharma Class 12 Maths Solutions Chapter 13 - Derivative as a Rate Measurer

1. What does the derivative of a rate mean?

The instantaneous rate of change is the measurement of the rate of change, or slope, of a curve at a certain instant. Thus, the instantaneous rate of change is related to the derivative. A derivative is a tool used to calculate the instantaneous rate of change of a variable with respect to another variable. The first-order derivative gives the slope of a tangent line. The average rate of change is different from the instantaneous rate of change. While the former gives the slope of the secant line which is usually calculated by algebraic formula the latter i.e. instantaneous rate of change gives the slope of the tangent line using derivatives.

2. What is the rate of change of y with respect to x, satisfying the rule y = f(x)?

The rate of change of y with respect to x means how much y changes per unit change in x. This means y is a function of x. Hence any change in x causes a change in rate.  Here, the rate of change of y can be found by taking the derivative of the original function y. It can be represented graphically also. The slope of the tangent line of the graph of y is plotted at the point where x=[x_{0}].

3. How do derivatives help in business?

Derivative has many real-life applications. Loss or profit in business can be calculated by derivatives. Derivatives are needed to maximize profit in business. Derivative of total profit with respect to the quantity has to be determined. This can be the way to find the profit-maximizing output. The derivative is taken as zero and quantity q is solved. Then the profit-maximizing quantity q is substituted with the demand value in the demand equation to get the value for profit output P. This way derivatization helps to get the maximum profit in business.

4. What are the applications of Derivative as a Rate Measure?

It is used to determine a new value of a quantity from the old value and the amount of change.

  • It helps us to calculate the average rate of change and explains how it differs from the instantaneous rate of change.

  • We can apply rates of change to the displacement, velocity, and acceleration of an object moving along a straight line.

  • It is also used to predict the future population from the present value and the population growth rate.

  • Derivatives are used to calculate marginal cost and revenue in a business situation.

5. How Vedantu helps the students in the Chapter of Derivative as a Rate Measure?

These solutions are formulated by Vedantu experts in an interactive manner to create interest in learning among students. Solutions provided by RD Sharma also contain explanatory diagrams and tables for comparative study, which makes it easy to learn the crucial topics. Students who find difficulty in solving these topics are suggested to go through solutions provided by RD Sharma. These solutions are prepared from the exam point of view and according to the latest syllabus. Vedantu also provides sample papers based on previous year’s questions on this topic to boost confidence regarding this topic among the students of Class 12.