How do you differentiate #y=ln[(x+9)^6(x+6)^2(x+5)^3]#?
First use properties of logarithms to expand this as a sum and then differentiate to get
Properties of logarithms allow us to write
Continuing, this is also equal to
This is now easy to differentiate (and the use of the Chain Rule is trivial) to get
Getting a common denominator gives
We continue to simplify: