Alternate Definition of Derivative
limit (as x approaches a number c)=f(x)-f(c)/x-c x≠c
In mathematics, the derivative of a function is a measure of how much the function changes as its input changes. It represents the instantaneous rate of change of a function at a particular point. An alternate definition of derivative can be understood as the slope of the tangent line to the graph of the function at that point. More formally, if we have a function f(x) and a point x = a, then the derivative of f at a is given by the limit:
f'(a) = lim (h → 0) [f(a + h) – f(a)] / h
This limit represents the slope of the secant line passing through the points (a, f(a)) and (a + h, f(a + h)), which becomes the tangent line at the point a as h approaches zero. Thus, the derivative of a function at a point is the rate at which the function is changing at that point. It is an important concept in calculus and is used in many applications such as optimization problems, curve sketching and physics.
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