Explore step by step the geometrical construction of the derivative of a function at a (draggable) point [color=#6aa84f][i]P[/i][/color].[br][br]The slider [color=#0000ff][i]h[/i][/color] represents the independent variable increment.

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