The product rule is defined as $$(f \cdot g)' = f' \cdot g + g' \cdot f.$$
I have the following function $u(x) = x\cdot \ln(3)$. I understand that you can derive it by implicit differentiation and have $\ln(3)$ as the result.
I, however, do not understand why I get the wrong result by applying the product rule:
$$ f(x) = x\\ g(x) = \ln(3)\\ f'(x) = 1\\ g'(x) = 1/3\\ D(f(x) * g(x))=\\ = 1 * \ln(3) + 1/3 * x \\ = \ln(3) + 1/3x \neq ln(3)$$