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) = x2-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.