Quotient Rule: Overview, Questions, Preparation

The Quotient Rule is a means to determine the derivative of a function, which is the ratio of two differentiable functions.

It is a basic rule used in differentiation problems where one function is divided by the other. The quotient rule follows the definition of the limit of the derivative. The quotient rule begins with the lower function, and it ends with the lower function squared.

Quotient Rule:

Let the function be denoted as m(x), given by:
m(x)= p(x)/ q(x).

Differentiating both sides, we get:

m’(x)= [p(x)/ q(x)]’ =  q(x),q’(x)- q(x).p(x)/ {q(x)}²

The ratio of two functions is equal to the ratio of differentiation of one function multiplied by the second function. Then, subtracting the product of differentiation of the second function and first function.

Proof from the Derivative Definition-

The topic “quotient rule” is a part of the chapter “Limits and Derivatives” in class 11 mathematics. This topic carries a weightage of around 4-5 marks in the examination.

1. Find the derivative of g(x)= (x+1)/x.

Solution:

2. Find the derivative of sin x.

Solution.

Q: What is the purpose of quotient rule?

Q: How can we define the limit of a function?

Q: What is the formula for derivative of a function?

Q: Which arithmetic properties are followed by functions?

Q: What are some standard derivatives?

A: