log differentiation

[calcstruggles2013]

is there a way to simplify this problem so it is easier to find the derivative?
I would assume you would bring down the exponents in front of whatever is in the parenthesis but you would still have to do a ton w product and quotient rules and it would get sloppy.

(100x+440)(7x-19)/((40x-40)(5x+45))

 

[tkhunny]

You seem to be suggesting that you have barely seen a logarithm.

\(\displaystyle \ln\left(\dfrac{A\cdot B}{C\cdot D}\right) = \ln(A) + \ln(B) - \ln(C) - \ln(D)\)

Where does that leave us?