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Differentiating ln x

Question 1 says to differentiate using the quotient rule f(x) = 1 + 2x/1-2x where x < 1/2. My answer is -8xsquared/1 - 2x squared.(at x = 1/4)

Question 2 says rewrite the expression of f(x) = ln (1 + 2x/1 - 2x) (-1/2 <x<1/2) by applying a rule of logarithm and then differentiate.
So rewriting f (x) = ln (1 + 2x) - (1 - 2x) = ln4x. Then if x = 1/4 f'(x) = 1/(1/4) = 4

Then the next part of the question asks-
Show that the function h(x) = 1 + 2x/1 - 2x - 2ln(1 + 2x/1 - 2x) (-1/2 <x<1/2)
has a single stationary point - find the value and determine the local max and local min. I have applied the quotient rule to the first 'bit' and for the 2ln 'bit' have an answer of 2(2/1 - 2x)
Then h'(x) = -8squared - 4/x to give -8x - 4 = 0
Any help would be appreciated.

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