`g(r) = r^2ln(2r + 1)` Differentiate the function.

You need to differentiate the given function, with respect to "r" variable, such that: `g'(r) = (r^2*ln(2r+1))'` Using the product rule, yields: `g'(r) = (r^2)'*ln(2r+1) + r^2*(ln(2r+1))'` You need to use the chain rule to differentiate the function `ln(2r+1)` , such that: `(ln(2r+1))' = (1/(2r+1))*(2r+1)'` `(ln(2r+1))' = (2/(2r+1))` `g'(r) = 2r*ln(2r+1) + (2r^2)/(2r+1)` Factoring out 2r, yields: `g'(r) = 2r*(ln(2r+1) + r/(2r+1))` Hence, evaluating the derivative of the given function, yields `g'(r) = 2r*(ln(2r+1) + r/(2r+1)).`