Move the slider [color=#1551b5][math]h[/math][/color], which represents the independent variable increment.[br]When [color=#1551b5][i]B[/i][/color] tends to [color=#c51414][i]A[/i][/color] along the function graph, line [color=#1551b5][math]r[/math][/color] tends to line [color=#1551b5][math]t[/math][/color], the tangent in [color=#c51414][i]A[/i][/color] to the curve.[br]The limit of the [i]difference quotient[/i], as [color=#1551b5][math]h[/math][/color] approaches 0, is the slope of the tangent to the curve in [color=#c51414][i]A[/i][/color].[br]You can also move the point [color=#c51414][i]A[/i][/color] along the function and explore how the slopes of [color=#1551b5][math]r[/math][/color] and of the tangent change accordingly.

Applying the definition, calculate the derivatives of the following functions, in the given points:[br][br][math]f(x)=\sqrt{3x-1} \mbox{ in } x=3[/math][br][br][math]f(x)=e^{2x} \mbox{ in } x=0[/math][br][br][math]f(x)=\frac{1}{1-x} \mbox{ in } x=2[/math]