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keketsu
Why is the derivative of (1-x)^3 negative? I can see 3(1-x)^2, but why -3(1-x)^2?
That's what the chain rule tells us. In other words, that is because the derivative of (1-x) is -1.
(U^n ) = n U^(n-1) * U' U = 1 -x -> U' = -1 => derivative result is negative!