How do I find the derivative of #lnroot3(4x5)((3x+8)^2)#?
1 Answer
Holy Jesus Christ!
Explanation:
First, let's identify it: it's a product which two terms will depend on chain rule. Thus, we'll need both two rules.

Product rule states that for
#y=f(x)g(x)# , then#(dy)/(dx)=f'(x)g(x)+f(x)g'(x)# 
Chain rule states that
#(dy)/(dx)=(dy)/(du)(du)/(dx)#
For the first term, let's rename
For the second term, let's rename
There's no need to derivate it completely straightforward. You can do steps separately, but I do think that that might confuse things a bit.
Substituting
Substituting
Substituting
Feel free to develop it, but this is fine as a final answer!