samuelson mathxp

For the past week or so, we’ve been focused primarily on differential calculus and becoming comfortable with the rules that have been derived through the limiting process. The derivatives of e^x and ln(x) were both derived but only the anti-derivative of the former reveals itself through that process. Since the primitive of ln(x) remains a mystery, only the first part of the exploration below can be tackled.

In order to facilitate completion of the entire sequence below, I will ask the students to determine the derivative of f(x)=-x+xln(x). The result will be very useful for our purposes here and will also launch us into Integration by Parts.

Thanks for reading.