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Basic Concept of Unitary Method/Chain Rule Video Lecture | Quantitative Techniques for CLAT

56 videos|104 docs|95 tests

FAQs on Basic Concept of Unitary Method/Chain Rule Video Lecture - Quantitative Techniques for CLAT

1. What is the basic concept of the unitary method/chain rule?
Ans. The basic concept of the unitary method/chain rule is to establish a relationship between different variables and use that relationship to solve mathematical problems. In the unitary method, we find the value of one unit and then use it to find the value of a given number of units. The chain rule, on the other hand, is a rule in calculus that allows us to find the derivative of a composite function by differentiating the inner and outer functions separately.
2. How is the unitary method applied in solving mathematical problems?
Ans. The unitary method is applied in solving mathematical problems by establishing a relationship between different variables. For example, if we know the cost of 1 kg of apples, we can use the unitary method to find the cost of a given number of kilograms of apples. By finding the value of one unit, we can then multiply it by the desired number of units to find the final answer.
3. Can you provide an example of applying the chain rule in calculus?
Ans. Sure! Let's say we have a function f(x) = (2x + 3)^2. To find the derivative of this function using the chain rule, we first differentiate the inner function (2x + 3) with respect to x, which gives us 2. Then, we multiply this result by the derivative of the outer function (2x + 3), which is 2(2x + 3). Therefore, the derivative of f(x) is 2(2x + 3) * 2 = 4(2x + 3).
4. What are some real-life applications of the unitary method?
Ans. The unitary method has various real-life applications. For example, it can be used in calculating the cost of materials needed for construction based on the cost of 1 unit of material. It can also be used in converting different units of measurement, such as converting pounds to kilograms or miles to kilometers. Additionally, the unitary method can be applied in solving problems related to speed, time, and distance.
5. How does the chain rule help in finding the derivative of composite functions?
Ans. The chain rule helps in finding the derivative of composite functions by breaking down the problem into simpler parts. It allows us to differentiate the inner and outer functions separately and then combine the results using multiplication. By applying the chain rule, we can handle more complex functions and find their derivatives efficiently.
56 videos|104 docs|95 tests
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