Find the derivative of f(x)= x^2/3(x^4/3-x^1/3+x^-5/3)

Assuming Lisa's interpretation of the statement of the problem is correct, this is a problem that was intended to demonstrate the value of remembering your algebraic manipulations while evaluating calculus expressions.

The product rule route creates a mess, as Lisa demonstrated with exacting attention to detail in her second evaluation.

By distributing, we see that a seemingly difficult expression becomes

f(x) = x

^{2}-x+x^{-1},quite quickly, which is a much easier expression to take a derivative of (mostly due to reduced opportunity to make an error). Of course the answers agree as they should.