Definition of Derivative
Move the slider , which represents the independent variable increment. When B tends to A along the function graph, line tends to line , the tangent in A to the curve. The limit of the difference quotient, as approaches 0, is the slope of the tangent to the curve in A. You can also move the point A along the function and explore how the slopes of and of the tangent change accordingly.
Applying the definition, calculate the derivatives of the following functions, in the given points: