Definition of derivative f'(x) =
f(a+h)-f(a)/h
The derivative of a function f(x) is a measure of the rate at which the function changes with respect to its input variable x. The derivative of a function f(x) with respect to x is denoted by f'(x). It is defined as the limit of the difference quotient of f(x) as the change in x approaches zero:
f'(x) = lim Δx→0 [f(x+Δx) – f(x)]/Δx
The derivative represents the slope of the tangent line to the graph of the function at a particular point, and thus it provides information about the behavior of the function in the neighborhood of that point. In particular, the derivative tells us whether the function is increasing or decreasing at a particular point, and how quickly it is doing so. It also allows us to determine the location of relative maxima and minima of the function. The derivative is an important tool in many fields of mathematics and science, including calculus, physics, economics, and engineering.
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