How do you differentiate #f(x)=sin2x * cotx# using the product rule?
1 Answer
Jan 24, 2016
Answer:
Explanation:

The product rule:
#d/(dx)[f(x)]=("derivative of the first term" * "the second term")+("derivative of the second term"*"the first term")# 
#d/dx[cotx]=csc^2x # 
#d/(dx)[f(x)]= (d/dx[sin(2x)]*cotx)+(d/dx[cotx]*sin2x)#
#=(2cos2x*cotx)+(csc^2x*sin2x)#
#=2cos2x*cotxcsc^2x*sin2x# 
You could just stop there, or you could simplify the answer further by uniting all the angles as
#x# using double angle formulas.