SSC CGL Exam > SSC CGL Videos > Quantitative Aptitude for SSC CGL > Chain Rule
Chain Rule Video Lecture | Quantitative Aptitude for SSC CGL
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FAQs on Chain Rule Video Lecture - Quantitative Aptitude for SSC CGL
| 1. What is the chain rule in calculus? |  |
Ans. The chain rule is a rule in calculus that allows us to find the derivative of composite functions. It states that if we have a composite function, such as f(g(x)), then the derivative of f(g(x)) with respect to x is equal to the derivative of f with respect to g multiplied by the derivative of g with respect to x.
| 2. How do you apply the chain rule in practice? | |
Ans. To apply the chain rule, you need to identify the inner and outer functions in a composite function. Then, take the derivative of the outer function with respect to the inner function and multiply it by the derivative of the inner function with respect to the independent variable. Finally, simplify the expression if possible.
| 3. Can you explain the concept of chain rule with an example? | |
Ans. Certainly! Let's say we have the function f(x) = (2x + 1)^3. To find the derivative of f(x), we can consider it as the composition of the inner function g(x) = 2x + 1 and the outer function h(x) = x^3. Applying the chain rule, we first find the derivative of h(x) with respect to g(x), which is 3(g(x))^2. Then, we find the derivative of g(x) with respect to x, which is 2. Finally, we multiply these derivatives together: 3(2x + 1)^2 * 2 = 6(2x + 1)^2.
| 4. What happens if you don't use the chain rule while differentiating a composite function? | |
Ans. If you don't use the chain rule while differentiating a composite function, you will end up with an incorrect result. The chain rule is essential in correctly determining the rate of change of a composite function because it takes into account the relationship between the inner and outer functions.
| 5. Is the chain rule applicable to all composite functions? | |
Ans. Yes, the chain rule can be applied to all composite functions, regardless of their complexity. It is a fundamental rule in calculus that enables us to find the derivative of composite functions and is widely used in various fields such as physics, engineering, and economics.
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Dec 23, 2024 Last updated |
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