Mathematical problems of derivative function, How to understand that the tangent equation of a given curve y = f (x) at x = 1 is y = X-1, Analysis shows that, f (1) = 0, f '(1) = 1,? This place does not understand, what is the relationship between the derivative function of the curve and the tangent, why f' (1) = 1, find the reasoning process

Mathematical problems of derivative function, How to understand that the tangent equation of a given curve y = f (x) at x = 1 is y = X-1, Analysis shows that, f (1) = 0, f '(1) = 1,? This place does not understand, what is the relationship between the derivative function of the curve and the tangent, why f' (1) = 1, find the reasoning process

For example, the tangent equation of y = f (x) at x = 1 is y = X-1, so the value of derivative function at x = 1 is 1, that is, f '(1) = 1