Quotient rule of differentiation. Today I will talk about the quotient rule of differentiation. Here it goes.

### Quotient rule of differentiation

Suppose is a quotient of two functions and . This means

Now my task is to differentiate , that is, to get the value of

Since is a quotient of two functions, I’ll use the quotient rule of differentiation to get the value of Thus will be

See also: Formulas for differentiation

There are two other rules in differentiation like product rule & chain rule.

Also, I have already written on the differentiation of different kinds of functions like implicit functions, logarithmic functions and parametric functions.

Now I’ll give you some examples of the quotient rule.

#### Some examples of quotient rule of differentiation

Here are some examples of the chain rule.

Disclaimer: None of these examples is mine. I have chosen these from some book or books. The references are at the end of the post.

##### Example 1

According to Croft et al. (2000) “Use the quotient rule to find the derivative of the following: .”

##### Solution

Here the given function is: .

First of all, I’ll give it a name, say .

So I can say .

Now is a quotient of two functions and .

In order to differentiate with respect to , I’ll use the quotient rule of differentiation.

Thus it will be

So this means

Now I’ll simplify it a bit.

Therefore it will be

Hence I can conclude that this is the answer to the first example.

Now I will go to the second problem.

Now I’ll go to the next example.

##### Example 2

According to Croft et al. (2000) “Differentiate … the following: .”

##### Solution

Here the given function is: .

First of all, I’ll give it a name, say .

So I can say .

Now is a quotient of two functions and .

In order to differentiate with respect to , I’ll use the quotient rule of differentiation.

Thus it will be

So this means

Now I’ll simplify it a bit.

Therefore it will be

Hence I can conclude that this is the answer to the second example.

Now I’ll go to the last example.

##### Example 3

According to Croft et al. (2000) “Use the quotient rule to find the derivative of the following: .”

##### Solution

Here the given function is: .

First of all, I’ll give it a name, say .

So I can say .

Now is a quotient of two functions and .

In order to differentiate with respect to , I’ll use the quotient rule of differentiation.

Thus it will be

So this means

Now I’ll simplify it a bit.

Therefore it will be

Hence I can conclude that this is the answer to the last example.

Dear friends, this is the end of my today’s post. Thank you very much for reading this. Please let me know how you feel about it. Soon I will be back again with a new post. Till then, bye, bye!!

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