Calculus ... Problem with simplifying

[K - Prime]

well ill go through the whole question up to where i am (not very far) to make sure there were no prior errors, but i cant simplfy past where i am (maybe i just cant see it)

Differentiate and simplify

.........(1-x)^4
f(x) = --------
...........1-4x

f'(x) = [4(1-x)^3(-1)](1-4x) - (1-x)^4(-4)
.........-----------------------------------
..........................(1-4x)^2

......= (-4)(1-x)^3 - (1-x)^4(-4)
.........------------------------- note: i cancelled the (1-4x) on top
.....................(1-4x) with one from the bottom


......= stuck (i tried common factoring on top but still cant get it)

any help will be GREATLY appreciated (last question on assignmentand driving me crazy)

sorry bout the formating, cant seem to get it right (hence the periods)

[vsage]

how'd you cancel out the (1-4x) from the top and bottom? (1-x)^4*-4 doesn't have (1-4x) as a common factor with the denominator. My personal suggestion (although lengthy to an extent) would be to expand all the numerator and see if it's divisible by 1-4x.

[BobG]

You can't cancel out the (1-4x) because it only appears on the left side of the numerator and not on the right. I don't see that much that's easily simplified (if you expanded the numerator so you could do the subtraction, it might simplify, but I doubt it).

[vsage]

Hrm I haven't really tried anything with it but see what happens when you factor out (1-x)^3 from the top from the left and right operands of the middle - sign.