Differentiate the function

Y = (8x^4-x+1) (-x^5+5)

First, multiply the brackets out:

(8x^4 - x + 1) (-x^5 + 5)

= - 8x^9 + x^6 - x^5 + 40x^4 - 5x + 5

Then, find f' (x) by multiplying each term by the power, then reducing the power by one:

f' (x) = - 72x^8 + 6x^5 - 5x^4 + 160x^3 - 5