Chain Rule
Que 1. What is Chain Rule?
Answer: The chain rule is used to calculate the derivative of composite functions like- (3×2 + 2x- 6)5, sin(x2 +5x), e2x, (4×2 +5x)(2x+6) etc. This chain rule is also referred to as the outside-inside rule, the composite function rule, or the function of a function rule. It is only used to determine the derivatives of composite functions.
Que 2. What is Chain Rule Formula?
Answer: The chain rule is used to calculate the derivative of composite functions (i.e when one function is inside the other). the chain rule formula is used in two ways:
d / dx (f(g(x))) = f' (g(x))·g' (x), dy/dx = dy/du . du/dx
Que 3. When to Use Chain Rule Formula?
Answer: When we have to find the derivative of the functions, which have a function inside functions (Composite function), we use the Chain rule formula, Because we don’t have a direct formula for composite functions, we have to use the Chain rule formula in that case.
The chain rule formula is : d / dx (f(g(x))) = f’ (g(x))·g’ (x),
Que 4. What are the applications of the Chain Rule Formula?
Answer: The chain rule is used as the main tool to solve Implicit Differentiation, Logarithmic Differentiation, Inverse Functions Differentiation, and Related Rates(rate of change of distance, rate of change of the average molecular speed, etc.).
Que 5. What is the difference between the chain rule formula and the product rule?
Answer: The chain rule formula is to find the derivative of a composite function(a function that is combined with other functions). ex- (2x2 + 5x – 6) while the product rule formula is used to find the derivative of the product of two or more functions. ex- (x +3). (x – 6).
The chain rule formula is d / dx (f(g(x))) = f’ (g(x))·g’ (x), while, The product rule formula is : d / dx (u.v) = u. dv/dx + v. du/dx
Chain Rule : Aptitude Questions and Answers
The chain rule is an important topic of Quantitative Aptitude that needs to be practiced well for competitive exams. The following article includes the concepts, steps, and formulas that are used to solve the chain rule questions.
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