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.