It measures how fast the inverse function changes with respect to its input, based on the rate of change of the original function.

The derivative of the inverse function at a point is the reciprocal of the derivative of the original function at the corresponding point.

No, the original function must be one-to-one and differentiable, and its derivative should not be zero at that point.

If the derivative is zero, the slope is flat, and the inverse function would not have a well-defined rate of change at that point.

It helps in solving problems involving logarithmic, exponential, trigonometric, and other inverse functions, especially when you need their slopes.