How do you differentiate #g(x) = [1 + sin(2x)]/[1  sin(2x)] # using the product rule?
1 Answer
Answer:
In order to forcedly use the product rule, we'll rewrite it as
Explanation:
Also, we'll need chain rule to differentiate the second term.

Chain rule:
#(dy)/(dx)=(dy)/(du)(du)/(dv)(dv)/(dx)# 
For the first term, we'll rename
#u=2x# 
For the second term, we'll rename
#v=(1sin(w))# and#w=2x# (but the logic follows the same way that of#u# ,#v# , and so on) 
Product rule:
#(ab)'=a'b+ab'#
Substituting