The Quotient Rule says that the derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator then all divided by the square of the denominator.
Reason for the Quotient Rule:
The Product Rule should be utilized when the derivative of the quotient of two functions is to be taken.
Method of Finding the Derivatives of Two Functions
It is expressed as:
- The denominator function times
- The derivative of the numerator function
- The numerator function times
- The derivative of the denominator function
- The square of the denominator function
Quotient Rules Calculus Examples
It is almost similar to the product rule in calculus. The only difference between the quotient rule and the product rule is that in the product rule we have the function of type f(x)*g(x) and in the quotient rule, we have the function of type f(x)/g(x).
This rule always starts with a denominator function and ends up with a denominator function.
Easy Steps to Find the Derivatives using the Quotient Rule
- Considering the given function, it should be in the form of division.
- Differentiating both sides of the function with respect to something.
- Suppose if the function on LHS is y equal to some other function of x.
- The derivatives on the RHS will be the lower function times the derivative of the upper function minus the upper function times the derivative of the lower function divided by the square of the lower function.
- The answer you will get at the end after the simplification will be the derivative of the function y which will be given to you.
Application of Derivatives in Real Life
Have you ever imagined that you will be using quotient rules in real life? If not, then let me tell you how.
Some examples are:-
- Calculating profit and loss in business using graphs.
- To check the temperature variations.
- Determining the speed or distance covered such as miles per hour, kilometer per hour, etc.
- Derivatives are also used to derive many equations in Physics.
- In the study of Seismology, to find the range of magnitudes of the earthquake.
Derivative Rules
There are three very important rules that are generally applicable and they depend on the structure of the function we are differentiating:
- The Product
- Quotient
- Chain Rules
Quotient Rule – Example
The quotient is the answer obtained when we divide one number with another.
For example, when dividing the number 6 by 3, we get the result as 2, which is the quotient. The quotient can also be an integer or a decimal number.
There are so-called “shortcut” rules for finding the derivative of a function. The quotient rule is a rule used to find the derivative of a function that can be written as the quotient of two functions. More simply, you can think of the quotient rule before applying to functions that are written out as fractions where the numerator and the denominator are both themselves functions.
Cuemath Classes
What are Cuemath classes all about? Have you heard about it? Now let me tell you what it is all about. Cuemath gives you a platform where you get the service of an online live education class which is created with the aid of subject-matter experts. A strong emphasis is given on the student’s idea clarity and ties theoretical doubts to real-world situations so that students may readily learn and grasp numerous concepts.
Cuemath classes are really different from other online classes. It distinguishes itself from the rest by adhering to five distinct fundamentals like instructional approach, class participation, subject focus, practice style, and end aim.
If you haven’t attended Cuemath classes then do attend it and am sure you would like these classes more than any other live classes out here.
