Researchers have found a correlation between respiratory rate and body mass in the first three years of life. This correlation can be expressed by the function log R(w) = 1.83 - 0.43 log(w), where w is the body weight (in kilograms) and R(w) is the respiratory rate (in breaths per minute).

(a) Find R′(w) using implicit differentiation.
(b) Find R′(w) by first solving the equation for R(w).