Your y'(x) is definitely not going to be that: I think the question is asking you to find the derivative of y(x) = 22^(x) instead of y(x) = log_22(x).
Here is the problem:
Use implicit differentiation to show (prove) that the derivative of y(x)=log 22 (x) is y'(x) = 22x ln (22).
Here is what I have done so far:
y(x) = (lnx)/(ln 22)
y'(x) = 1/(x ln 22).
but I do not get what is asked for.