For implicit differentiation, you are using the chain rule

Except u(x) = y, So after every "y" term is differentiated it will be multiplied by dy/dx.
17)

Then you solve for dy/dx as if its a variable.

18) Here lets review product rule:

Take derivative of each term

Solve for dy/dx using factoring:
Well I know you said dont answer with subtraction and adding but thats how you do it... 1 more student likes read more than yellow
7-6.. is 1
6+1.. is 7
Dont know how else to tell ya