How to get the exact differential in three variables. Hello friends, today I’ll show how to determine the exact differential in three variables. Have a look!!

**How to get the exact differential in three variables**

If any function is dependent on three real variables

Now the differential

If interested, you can read more on * how to get the differential dz of a function*.

Therefore the differential

If interested, you can also read more about the * exact differential in two variables*.

Now I’ll give an example of how to determine the exact differential in three variables.

**An example of how to determine exact differential in three variables**

Note: This example is not mine. I have chosen it from some book. I have also given the due reference at the end of the post.

So here is my example.

**Example **

According to Stroud and Booth (2011)* “Verify that

**Solution**

So here the given differential is

Now I compare it with the standard form of the differential

First of all, I’ll differentiate

(1)

Next, I’ll differentiate

(2)

Then I’ll differentiate

(3)

Now I’ll differentiate

(4)

Next, I’ll differentiate

(5)

Finally, I’ll differentiate

(6)

As I can see from both equations (1) and (3) that

Also I can compare both equations (2) and (5) to see that

Again I can see from both equations (4) and (6) that

Hence I can conclude that the differential

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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