Ah, which is where you've gone wrong.
Just differentiate it normally...
then
You missed a minus sign in the above, otherwise correct.
ln 2/x = -1/x
For your original question... Fine, but learn how to properly write it out as you'll get probably close to 0 for the above type of working. It makes no mathematical sense although I know what you are saying with it.
y = ln(3x+4)^4
= 4 * ln(3x+4)^3 * 3/(3x+4)
= 12 ln(3x+4)/(3x+4)
I'm sure you are aware that the derivative of x^n = nx^(n-1) * 1 since 1 is the derivative of x.
Same thing applies for functions.
Derivative of (some function)^n = n((some function)^(n-1) * derivative of (some function)
Or in maths notation.