calculate derivative of f(x)=5x (x-1)^4

We also could expand the binomial and then we'll
differentiate each term of the polynomial.

(x-1)^4 = x^4 -
4x^3 + 6x^2 - 4x + 1 (1)

Now, we'll multiply (1) by
5x:

5x(x-1)^4 = 5x(x^4 - 4x^3 + 6x^2 - 4x +
1)

5x(x-1)^4 = 5x^5 - 20x^4 + 30x^3 - 20x^2 +
5x

We'll differentiate with respect to x and we'll
get:

f'(x) = 25x^4 - 80x^3 + 90x^2 - 40x +
5

We'll factorize by
5:

f'(x) = 5(5x^4 - 16x^3 + 18x^2 - 8x +
1)