What is the differentiation of 2lnx/3?

Assuming your question is to find the derivative of 2ln(x/3), not (2/3)lnx:
You can factor out the 2, so your answer will be twice the derivative of ln(x/3).

To differentiate this, use the chain rule where u=x/3, so du/dx = 1/3 and dy/du = 1/u

So dy/dx = (1/3)*(3/x) = 1/x. Multiply by the one to get the answer of 2/x.

Sorry if I got the wrong one... But your question is a bit ambiguous. I saw a previous answer got you the other one, so you have the right answer either way!

differentiation of (lnx) = 1/x

take the constant 2/3 out of lnx

so the final answer is 2/3* 1/x = 2/3x