Explore the geometrical construction of the derivative of a function at a (draggable) point [color=#1e84cc][b][i]P[/i][/b][/color].[br][br]The slider [b][color=#1e84cc][i]h[/i][/color][/b] 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]