Understanding of Derivative of a Function as its Gradient Function.[br] (Please use Java applet mode to run applet, as it is not HTML5 ready due to use of Latex for display of calculation text )[br]Try various input functions and check for yourself how the gradient of the tangent to the curve at a point P [br]is related to the derivative of the function.

1. Input a function in x[br]2. Move slider n to select the position of point P on the curve of the function[br]3. Click on checkbox for Tangent at P and Gradient at P to show the gradient graphically[br]4. Click on checkbox for Text on Derivatve to see the differentiation of the given function[br]5. Click on checkbox for Curve of Derivative Function to show the graph of the derivative function f'(x)[br]6. Click on the checkbox for Point on Curve of Derivative function to see how the gradient of the derivative function can be obtained from the y coordinate [br] of the derivative function for the same x coordinate for P[br]7. Click on checkbox for Calculation of Gradient to see how the substitution of the x coordinate value into derivative function gives[br] the answer for the gradient at P.