Definition of the Derivativef'(x) = ___________________
lim h->0 f(x+h)-f(x) / h
The derivative of a function f(x) at a point x is defined as the instantaneous rate of change of the function with respect to x at that point. It is denoted by f'(x) and is mathematically expressed as the limit of the difference quotient (f(x + h) – f(x))/h as h approaches zero:
f'(x) = limit[(f(x + h) – f(x))/h] as h approaches 0
In simple terms, the derivative of a function at a point gives the slope of the tangent line to the function at that point. It is a fundamental concept in calculus and finds wide applications in fields such as physics, engineering, economics, and computer science.
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