# First derivative

1. Feb 27, 2010

### shanshan

1. The problem statement, all variables and given/known data
differentiate f(x) = [2x^(2/3)][3-4x^(1/3)]

2. Relevant equations

3. The attempt at a solution
f'(x) = (4/3)(x^(-1/3))(3-4x^(1/3)) + (1/3)(-4)(x^(-2/3))
= 4x^(-1/3)-(16/3)-((4/3)(x^(-2/3)))
= (4/x^(1/3))-(16/3)-(4/3(x^(-2/3)))
I'm pretty sure I've made a mistake, but I can't find it.

2. Feb 27, 2010

### jgens

Remember, the product rule is defined as $f' = g'h + gh'$. When you used the product rule, you forgot to multiply the second term by $2x^{2/3}$.