The derivative is the instantaneous rate of change, defined by the limit of the difference quotient as the increment 'h' approaches zero. Option A is the standard mathematical definition. Option B is incorrect because it uses f(x-h) - f(x) which would lead to the negative of the derivative unless the denominator was also -h. Option C is incorrect because the numerator must represent the change in y (difference), not the sum. Option D is incorrect because h must approach 0, not infinity, to find the slope at a specific point.