Monday, March 18, 2013

Differentiation - Calculus

In calculus, a branch of mathematics, the derivative is a measure 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 a moving object with respect to time is the object's instantaneous velocity.

The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. Informally, the derivative is the ratio of the infinitesimal change of the output over the infinitesimal change of the input producing that change of output.

For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point.

Differentiation is the process of finding a derivative


1. Open a new geogebra file.( Applications --> Education --> Geogebra)
2. Click once in the Input Field and enter the function f(x)=sin(x)
3. Type f '(x)  into the input bar. The software automatically calculates the derivative of f(x)
4. Select the New Point tool and click anywhere on the graph of f(x). The new point is A
5. Select the Tangents tool, then click on the point and on the function f(x).
6. Select the Slope tool and click on the line (Tangent)
7. In the input bar, type (x(A),m) where m is the slope of the tangent.  This creates a point B whose x-coordinate is the x-coordinate of A and y-coordinate is m.  As we drag point A, point B follows the derivative curve
8. Right click the point B and select Trace On. Now, as A is dragged, B leaves a record of its path.  We can hide/unhide the graph of f '(x) to conform that this is really the graph of the derivative.

Click here

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