We know from the Power Rule for rational exponents that the functions in the list have derivatives `3 t^2,` `3.1 t^(2.1),` `3.14 t^(2.14)`, and so on. In Activity 3 we saw that, for each value of `t`, the slopes of the approximating functions approach the slope of the limiting function. That is, the derivative of `t^(pi)` is the limiting value of `3 t^2,` `3.1 t^(2.1),` `3.14 t^(2.14), ... .` In short,