Expert: Sherman D. - 1/1/2006

Question
my work out (a),use quotient rule to differentiate the function f(x)=1+2x/1-2x
  let u=1+2x,du/dx=2,let,v=1-2x,dv/dx=-2
      f(x)=(1-2x)(2)-(1+2x)(-2x)/(1-2x)^2
          =2-4x+2+4x/(1-2x)^2
           =4/(1-2x)^2
b,if you have been told to use composite rule and your answer to part(a) to differentiate the function g(x)=In(1+2x/1-2x)how can you combine them together? can you hint me how to tackle such a problem like this.

Answer
Sorry it took so long, i had to get some help to make sure i understood your question a little better.

We already know a. is correct.

g(x) = ln((1 + 2x)/(1 - 2x))

g'(x) = ln'(f(x)) * f'(x)
g'(x) = (1/(f(x))) * f'(x)

g'(x) = (1/((1 + 2x)/(1 - 2x))) * (4/(1 - 2x)^2)
g'(x) = ((1 - 2x)/(1 + 2x)) * (4/(1 - 2x)^2)
g'(x) = (4(1 - 2x))/((1 + 2x)(1 - 2x)^2)
g'(x) = (4(1 - 2x))/((1 + 2x)(1 - 2x)(1 - 2x))
the (1 - 2x)s cancels out
g'(x) = 4/((1 + 2x)(1 - 2x))