Basic Derivative
f(x^n)= nX^(n-1)
The derivative is a mathematical concept used in calculus to represent the instantaneous rate of change of a function with respect to one of its variables. Put simply, the derivative of a function f(x) is the slope of the tangent line to the curve at a given point x.
The basic formula for the derivative of a function f(x) is:
f'(x) = lim[h→0] (f(x+h) – f(x))/h
This formula represents the limit as h approaches 0 of the difference quotient, which is a measure of the average rate of change of f(x) over the interval [x, x+h]. As h approaches 0, this interval shrinks down to a single point, and the difference quotient approaches the instantaneous rate of change of f(x) at that point.
In practical terms, this means that to find the derivative of a function, you take the limit as the interval over which you are measuring the rate of change approaches 0. This can be done algebraically or graphically, and the resulting derivative function can be used to analyze the behavior of the original function in a variety of ways, including finding extremes (maximums and minimums), inflection points, and concavity.
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