The derivative of 1 with respect to x is zero, since the derivative of any constant function is zero. So you must be saying that the derivative of 1/f(x) with

The derivative of 1 with respect to x is zero, since the derivative of any constant function is zero. So you must be saying that the derivative of 1/f(x) with respect to x is zero for any f(x), where f is a differentiable function, with non-vanishing derivative near x (for it to be defined in the first place). That doesn't make any sense. Please don't respond to this. It's getting absurd.