Find the derivative of the function

The derivative of y in terms of x is denoted by  or .

 For the given problem: , we may apply the basic differentiation property:  .

Apply the basic differentiation property:

For the derivative of , we may apply again the basic derivative property: .

For the derivative part, follow the basic derivative formula for natural logarithm function: .

 Let then .

 Note For the derivative of ,we apply the Quotient Rule: .

Let:

then

then

Then,

                

                 

               

Applying:  on:

                                     

                                     

Cancel common factors 2 and from top and bottom:

Recall then the derivative becomes:

For the derivative of  , we apply basic derivative formula for inverse tangent:

Combining the results, we get:

or