In mathematics, the quotient rule is used in calculus for the differentiation of quotients. It is a method for determining the derivative or differentiation of a function which is expressed in the form of the ratio of two differentiable functions. Functions often come as quotients that mean one function is divided by another function. Quotient rule is the most established rule used in solving the problems involving differentiation in which one function is divided by the other function.
For example, y = cos x/ x is a function that can be written as y = m/n where we consider cos x as ‘m’ and x as ‘n’. So the function has a numerator function and a denominator function. The quotient rule or formula is applicable for the differentiation of quotients that have a numerator and a denominator.
Quotient rule in calculus is a method to find the derivative or differentiation of a function that can be expressed in the form of a ratio or division of two functions both of which are differentiable. In other words, the quotient rule gives a method for differentiating the division of functions or the quotients.
Therefore, we can apply the quotient rule when we have to find the derivative of a function of the form of f(x)/g(x), such that g(x) ≠ 0 and both f(x) and g(x) can be differentiable.
More About Quotient Rule
A Quotient Rule states how to denote the differentiation of a given function that is expressed in the form of a ratio of two functions. An important aspect of the quotient rule is that it begins with the bottom function and ends with the bottom function squared. The quotient rule can be written as follows:
[(The quantity of the denominator) x (The derivative of the numerator function) – (The quantity of numerator) x (The derivative of the denominator function)] / (square of the denominator function)
For example, if a function is expressed as the ratio of two functions f(x) and g(x), then as per the quotient rule the derivative or differentiation of the function f(x)/g(x) is determined by the following steps:
- Take the derivative of f(x) and multiply it by f(x)
- Take the product of f(x) and the derivative of g(x) and subtract it from the product obtained in step 1
- The expression thus obtained in step 2 is divided by g(x) squared.
Mathematics can be a very interesting subject to those who can understand the concepts. The subject can be learned from a very early age using real-life examples and application-based tools that make the subject interesting and easy to learn. Practicing problems apart from the math classes act as a supplement to learning the subject rather than memorizing it. Students have to build a strong foundation in mathematics from the early standards under the guidance of efficient mentors and teachers. Then they would be able to solve problems conveniently through simple steps.
Therefore, the basic focus of learning mathematics is to develop conceptual clarity which involves efforts and interest from both the teachers as well as students. Teachers must analyze the students’ ability to assimilate the learning and apply some simple methodologies that help students to learn the concepts conveniently. The students should also keep on practicing for further improvement on weak areas. The aim of practice-oriented learning in mathematics is to develop problem-solving skills to handle problems with better speed and accuracy.