Quotient Rule of Derivative
What is Quotient Rule of differentiation?
Quotient rule of differentiation is the rule that is used to find the differentiation of the function which is given in the quotient form, i.e. a function given as the division of two functions.
What is Quotient Rule Formula?
Quotient Rule Formula is,
f'(x) = [u(x)/v(x)]’ = [u'(x) × v(x) – u(x) × v'(x)] / [v(x)]2
This formula gives the differentiation of the function that is represented as f(x)/g(x).
How to Derive the Formula of Quotient Rule?
Quotient rule can be derived using three methods,
- By Derivative and Limit Properties
- By Implicit Differentiation
- By Chain Rule
How to Use Quotient Rule?
Quotient rule is used to find the differentiation of the function expressed as the division of two functions that includes, all the functions of form f(x) and g(x) such that individual differentiation of f(x) and g(x) exist and g(x) can never be zero.
How do you find the Derivative of a Division Function?
Derivative of the division function is easily found using the quotient rule formula, i.e. if we have to find the differentiation of H(x) such that H(x) is expressed as H(x) = f(x)/g(x) then its derivative is expressed as,
H'(x) = d/dx [f(x)/g(x)] = [f(x) × g'(x) – g(x) × h'(x)] / [g(x)]2
What is the Limit of Quotient Rule?
Quotient Rule for limits states that the limit of a quotient functions equals the quotient of the limit of each function.
Quotient Rule: Formula, Proof, Definition, Examples
Quotient Rule is a method for finding the derivative of a function that is the quotient of two other functions. It is a method used for differentiating problems where one function is divided by another. We use the quotient rule when we have to find the derivative of a function of the form: f(x)/g(x).
Let’s learn about the Quotient Rule in Calculus, its formula and derivation, with the help of solved examples.