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en.wikipedia.org/wiki/Derivative

The most common approach to turn this intuitive idea into a precise definition is to define the derivative as a limit of difference quotients of real numbers. This is the approach described below. Let f be a real valued function defined in an open neighborhood of a real number a. In classical ...

tutorial.math.lamar.edu/Classes/CalcI/DefnOfDerivative.aspx

In the first section of the last chapter we saw that the computation of the slope of a tangent line, the instantaneous rate of change of a function, and the instantaneous velocity of an object at all required us to compute the following limit. We also saw that with a small change of notation this limit could also be written as,. (1) ...

tutorial.math.lamar.edu/Problems/CalcI/DefnOfDerivative.aspx

The Definition of the Derivative. Use the definition of the derivative to find the derivative of the following functions. 1. [Solution]. 2. [Solution]. 3. [Solution]. 4. [ Solution]. 5. [Solution]. 6. [Solution]. 7. [Solution]. 8. [Solution]. 9. [Solution]. 10. [ Solution]. 11. [Solution]. Problem Pane. Decrease Problem Pane. Increase Problem Pane.

Just a philosophical digression. If mathematicians until today don't know how to define a process like division by zero, isn't it impossible to assume that if a division by zero has any kind of definition, humanity can never surely estimate. It seems kind of strange that the financial sector, higher analysis and modelling relies on ...

The derivative of function f at x=c is the limit of the slope of the secant line from x= c to x=c+h as h approaches 0. Symbolically, this is the limit of [f(c)-f(c+h)]/h as h→ 0.