We notice that we'll have to find the derivative of a
fraction, so, we'll have to use the quotient rule.
(u/v)' =
(u'*v - u*v')/v^2
We'll put u = 2x^2 + 1 => u' =
4x
We'll put v = 2x^2 - 1 => v' =
4x
We'll substitute u,v,u',v' in the formula
above:
f'(x) = [4x*(2x^2 - 1) - (2x^2 + 1)*4x]/(2x^2 -
1)^2
We'll factorize by
4x:
f'(x) = 4x(2x^2 - 1 - 2x^2 - 1)/(2x^2 -
1)^2
We'll combine and eliminate like terms inside
brackets:
f'(x) = 4x *(-2)/(2x^2 -
1)^2
f'(x) = -8x/(2x^2 -
1)^2
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