RD Sharma Solutions Class 12 Maths Chapter 12 - Higher Order Derivatives - Free PDF Download
Derivatives are important because they give an instant idea about the rate of change and help in determining the desired quantity in any real-life problem. Higher-order derivatives mean derivatives of derivatives. Second-order derivatives are important for their physical interpretation and are often used in modeling transportation devices. This chapter has an important weightage in the Class 12 syllabus and engineering competitive exams.
Chapter 12 which deals with Higher Order Derivatives which is a very important concept not only from the exam point of view but also from the career point of view.
Differentiation can proceed several times in succession. A succession of differentiation that is derivative of the derivative is referred to as higher-order derivatives. A second-order derivative is important for its physical interpretation. This is important because the information which first-order derivatives cannot provide is given by second-order derivatives. For instance, when the rate of change is zero, first-order derivatives cannot differentiate between local minima and maxima and have to depend upon higher-order derivatives for this. Newton updated his approach with the use of second-order derivatives.
When a function say y=f(x) is differentiated we get a first derivative or first order derivative denoted by y’ or f’(x) and when we again differentiate the derivative obtain with respect to x we get second derivative or second order derivative denoted by f’’(x) or y’’. Remember same derivative rules are applied for higher order derivatives as for first derivative or first order derivatives.
Higher Order Derivatives are an important chapter in both boards and competitive exams. It is recommended to cover thoroughly to ensure full marks in exams. Previous years’ question pattern shows that this chapter has a good weightage in the JEE Main paper. If not more but one question is sure in JEE Main and that can be a sure score. The clear concept of this chapter also helps in scoring a couple of more answers related to this chapter. Altogether 10-12 marks can be easily scored from a thorough knowledge of Higher Order Derivatives. This chapter can bring marks without consuming much time so this chapter is quite important for the students.
RD Sharma for Higher-Order Derivatives
Higher-Order Derivatives is an important chapter and so every means should be taken to score full from this topic. NCERT guidelines can build basic concepts. However Higher Order Derivatives at JEE level need more practice. RD Sharma can be an option but Arihant and MTG books will be best for practicing and having depth knowledge in this chapter. This topic needs to develop sound concepts as many other chapters both in Math and Physics depend upon an understanding of this chapter. To build that extra confidence in this topic, solving a lot of sample papers and the last 10 years’ JEE question papers is a must.
If the original function is increasing or decreasing with respect to a variable is determined by derivatives. Higher-order like second-order derivatives can express how the graph gets curved, determining if the function is concave upwards or downwards. This gives a very good physical interpretation. For Example, suppose in the Corona Pandemic two graphs have been prepared, one showing concave up and the other concave down. In both the graphs, the number of people getting affected and the rate of people getting affected may be the same so here the first derivative cannot gather much information. However, the nature of the curve will decide whether the steps taken to combat the disease are working or not. Concaving upwards means the measures are not working while the downwards concave indicates the rate is decreasing and hence the disease is trailing off. Hence graphs are an easy and important way to determine higher-order derivatives.
Vedantu for Higher-Order Derivatives
Experts of Vedantu have tried every means to help the students to crack competitive exams and even score well in their board exams. Keeping the student’s improvement in mind they provide PDF versions of important math books like RD Sharma which are easily downloadable free of cost from their site for conceptual learning. RD Sharma has given a few examples which are very important for solving and practicing. The workout is given in such a way that the students can understand them even in the first attempt they cannot answer them. Vedantu experts have also done research on the last 10 years' question papers and prepared sample papers for the students from the experience they gathered from the research. They are also available for any sort of doubt clearance for the students to build solid concepts on important chapters.