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)).`
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