It doesn't invalidate the rule, it just checks if you understood differentiation as an operator and not as a procedure. The general approach is to take an equa

It doesn't invalidate the rule, it just checks if you understood differentiation as an operator and not as a procedure. The general approach is to take an equation involving a function and differentiate that equation then factor the equation to find the derivative. It usually only comes up if finding a closed form expression for the function is intractable but factoring the derivative of a known equation involving the function is tractable. If the function is vector valued or tensor valued, even that can be intractable since it might be difficult to factor the equation after differentiating to isolate the derivative you want an expression for. I also don't use it very often, but it is invaluable in differential geometry and provides (for example) an easy way to derive an expression for the derivative of a determinant or the derivative of an inverse with respect to a tensor.