Chapter 7.1, Problem 76E

Alternative proof of product property Assume that y > 0 is fixed and that x > 0. Show that $\frac{d}{dx}(\ln xy)=\frac{d}{dx}(\ln x)$. Recall that if two functions have the same derivative, then they differ by an additive constant. Set x = 1 to evaluate the constant and prove that ln xy = ln x + ln y.