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Guillermo Marín
Roberto Loo
Karen Chen

Benjamin Sosa





In this investigation we will explain the term derivative.

Derivative is in calculus (a branch of mathematics) the derivative is ameasure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example,the derivative of the position of an object with respect to time is the object's instantaneous velocity.


Differentiation is a method to compute the rate at which a dependentoutput y changes with respect to the change in the independent input x. This rate of change is called the derivative of y with respect to x. In more precise language, the dependence of y upon x means thaty is a function of x. This functional relationship is often denoted y = ƒ(x), where ƒ denotes the function. If x and y are real numbers, and if the graph of y is plotted against x, the derivativemeasures the slope of this graph at each point.
The simplest case is when y is a linear function of x, meaning that the graph of y against x is a straight line. In this case, y = ƒ(x) = m x + b, for realnumbers m and b, and the slope m is given by

The derivative as a function
Let ƒ be a function that has a derivative at every point a in the domain of ƒ. Because every point a has a derivative,there is a function that sends the point a to the derivative of ƒ at a. This function is written f′(x) and is called the derivative function or the derivative of ƒ. The derivative of ƒ collects all thederivatives of ƒ at all the points in the domain of ƒ.
Sometimes ƒ has a derivative at most, but not all, points of its domain. The function whose value at a equals f′(a) whenever f′(a) is defined...
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