General Power Rule

[Mabeuf]

I am stuck.

My homework question is: Use the General Power Rule to find the derivative of the function

h(x) = (4x-x^2)^3
so I do the following:
h'(x) = 3(4x-x^2)^2 d/dx(4x-x^2)
= 3(4x-x2)^2(4-2x)

I think I am missing something because the previous problem with the solution provided is

h(x) = (6x - x^3)^2

h'(x) = 2(6x-x^3)d/dx(6x-x^3)
= 2(6x-x^3)(6-3x^2)
It then gives this as the solution:
=6x(6-x^2)(2-x^2)
I have no idea where the heck this came from.

My assumption based on the above answer is that the solution to my original problem would be
4x(4x-x^2)(4-x^2) but I don't know why.

Please help!

 

[royhaas]

The only thing missing is some factoring. \(\displaystyle h'(x) = 2(6x-x^3)d/dx(6x-x^3)=2(6x-x^3)(6-3x^2)=2x(6-x^2)(3)(2-x^2)=6x(6-x^2)(2-x^2)\).

 

[Mabeuf]

Gee aren't I smart. Thanks.