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What is the Quotient Rule?

The literal meaning of the term ‘quotient’ is the quantity that we get after two numbers are divided. It also signifies the integer part of the arithmetic operation division. A rule which is used to determine the differentiation of two numbers in the form of a ratio is defined as the quotient rule. It can also be regarded as the formula used to divide one derivative function from the other function. This rule follows the rule of product which is known as the product rule and the limit derivation concept. We can prove the quotient rule by the help of various methods such as: using the chain rule, using the implicit differentiation rule, and the properties of derivatives and limits. In this article, we will try to cover some concepts related to the quotient rule and do a brief analysis of them.

What is Differentiation?

In the paragraph mentioned above, we wrote that the quotient rule is used to determine the differentiation of two numbers in a form or ratio, but do you know what is differentiation? No!. Let me tell you, the term differentiation basically signifies the process through which we find the function of the derivative. This term has extensive use in calculus and the world of physics. The process opposite to finding the derivatives is defined as the anti-differentiation. Some examples are as follows: the rate of the change of displacement with the respect of time given ‘t’ is known as the velocity. The standard unit of velocity is meter per second square units. Let us assume that there are two variables, a and b. The variable a is changing time with respect to variable b, therefore the formula given is da/dx Or dy /dx if the variables are x and y respectively.

Various Types of Differential Rules

As mentioned above, differentiation is a process used to determine the function of the derivative. In the next points, we will try to cover the types of differential rules which include the rule of quotient which is the center of attraction in this article. The following points mentioned below analyses those types.

  • A rule used to determine the differentiation of two numbers in the form of a ratio is defined as the quotient rule.
  • A rule which is used to find the differentiation or derivative of a function that has been formed due to the multiplication of two functions that are differentiable is known as the product rule.
  • A differential rule used to determine the value of the composite function is defined as the chain rule. It is also known as the composite rule of function or inside-outside rule.read more : newsmartzone

Some Frequently Asked Questions about the Quotient rule

In this section, we will deal with the questions which are generally asked about the quotient rule.

Question 1.  How to use the process of quotient rule to differentiate?

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We know that the conversion of the ratio of two numbers and applying them into the formula of the quotient rule will differentiate the function given.

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Question 2. Name the rule used to find the derivative of product and division function?

The rule which is used to find the derivative of product function and division functions is product rule and quotient rule respectively.

Question 3. Which rule is also known as the rule of composite function or inside-outside function?

The chain rule is regarded as the composite rule and inside-outside rule.

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