The derivative of a point on a curve is essentially the tangent slope of the curve at that point, and the definition of derivative is given from that point, that is, another point on the curve is chosen to connect two points near that point (called secant). When another point approaches the desired point, the secant will gradually approach the tangent of the desired point, and the slope value of the secant will also approach the slope value of the tangent. There is no problem with the definition of derivative in the title. The fraction in the limit sign represents the above secant slope, where 6 is the desired point and 2+2x is another point. When x approaches 2, 2+2x will approach 6, and the secant slope (i.e. the value of the fraction) will approach the tangent slope value 6 (i.e. the derivative value of 6).