Logarithmic differentiation of functions. Hello friends, today I will talk about the logarithmic differentiation of functions. Have a look.

### Logarithmic differentiation of functions

The standard formula for the logarithmic differentiation of functions is like this:

for

See also: standard formulas for differentiating functions

Now I’ll show you how to use this formula to differentiate any logarithmic function.

Here I will solve two problems for you.

#### Examples of the logarithmic differentiation of functions

Disclaimer: None of these examples are mine. I have chosen these from some book or books. I have also given the due reference at the end of the post.

So here is the first example.

##### Example 1

According to Stroud and Booth (2013)* “Differentiate .”

##### Solution

Here the given function is: .

First of all, I’ll simplify the function .

For that, I’ll use the standard formulas for logarithmic functions.

See also: formulas for logarithmic functions

###### Step 1

So, at first I’ll use the formula

Thus the given function will be

Now I’ll use the formula

Therefore the function will be

Next, I’ll use the formula

Also I’ll substitute in the function.

Thus the given function will be

I can also rewrite the function as

(1)

Now I’ll go to the next step.

###### Step 2

So I’ll differentiate the equation (1) with respect to to get

Thus it will be

Now I’ll simplify it to get

So this means

which in turn gives

And this means

Thus the final value of will be

And this is the answer to the given example.

Now I will give another example.

##### Example 2

According to Stroud and Booth (2013)* “Differentiate .”

##### Solution

In this example, the given function is: .

Like the first example, here also I’ll simplify the function first.

For that, again I will use formulas for logarithmic functions.

###### Step 1

First of all, I’ll use the formula

Thus the given function will be

Next, I’ll use the formula

Now the function will be

Again I can write as

Therefore the function will look like

Once more I’ll use the formula so that the given function will be

(2)

Now I’ll go to the next step.

###### Step 2

Here I’ll differentiate equation (2) with respect to to get

So this gives

Now I’ll simplify it to get

So this means

which in turn gives

And this brings the final value of as

This is the answer to this problem.

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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