Differentiate f = ln(x^2 + 1) / (x ^ 2 + 1).
We'll apply the quotient rule using "u = ln(x2 + 1)" and "v = x2 + 1". First we'll need to calculate u' and v'.Using normal differentiation rules, we can see "v' = 2x". Now the rule for differentiating ln(f(x)) is f'(x) / f(x), so using this we can calculate "u' = 2x / (x2 + 1)".Now we can apply the quotient rule f'(x) = (u'v - uv') / v2 to calculate f'(x). So u'v = (2x / (x2 + 1)) * (x2 + 1) = 2x. And uv' = ln(x2 + 1) * 2x. So f'(x) = (2x - 2xln(x2 + 1)) / (x2 + 1)2.
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