Differentiate f(x)=2x^(2/3)(3-4x^(1/3))

[shanshan]

Homework Statement

differentiate f(x) = [2x^(2/3)][3-4x^(1/3)]

Homework Equations

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.

 

[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}.