The difference quotient is the slope of a secant line.to derive it, you would find the slope of a secant line.for the slope formula, to find the value of m, you use y-y1/x-x1. Start with the y axis to find the coordinates.first point is x and the distance between that point from another point is h.the second point is x+h.to find the value of y,, if you start at x, the value going up would be f(x) because its a function.then you plug in the expression x+h into f(x) to find the second point.so in the end the coordinates are (x,f(x)) and(x+h,f(x+h)).plug these coordinates into the slope formula and you will get the derivative formula.

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