Quotient rule of differentiation. Today I will talk about the quotient rule of differentiation. So here it goes…

Looking for more rules in differentiation? Do check-in:

**Product rule of differentiation**

If you’re interested to find out more about the differentiation of functions, here you go…

**Differentiation of parametric functions **

**Differentiation of implicit functions**

**How to differentiate of logarithmic functions**

**READ, DOWNLOAD & PRINT – Quotient rule of differentiation (pdf)**

**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**

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

**Some examples of the quotient rule of differentiation**

Here are some examples of the quotient rule of differentiation.

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**

Now 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 .

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 to get

And that means

Thus the derivative of is

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

Now I’ll give another example.

**Example 2**

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

**Solution**

So here the given function is: .

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

Thus I can say .

Now is a quotient of two functions and .

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

Thus it will be

So this means

Next, I’ll simplify it.

And that means

Also I can rewrite it as

Since , I can say that

So this gives

Therefore the differentiation of is .

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

Now I’ll give another example.

**Example 3**

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

**Solution**

Now here the given function is: .

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

So I can say .

Also, is a quotient of two functions and .

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

Thus it will be

So this means

Next, I’ll simplify it.

And that means

Now I’ll remove the round brackets to get

So this means

Therefore the derivative of is .

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

Dear friends, this is the end of 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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