Based on your work you are not using the correct formula. What follows next is what you should do to update all your other formulas.
[math] If\ y = A\log_eU,\ then\ y' = \dfrac {A}{U}\dfrac{dU}{dt}[/math]. So in all your derivative formulas you should replace all x's (or t's or q's,...) with U and then multiply by dU/dx (or dU/dt or dU/dq,...)
In your case U = 2t. So [math]\dfrac{dU}{dt}\ =\ 2[/math]