#f(x) = (x^2 + 1) * (5x^4 + 2x + 3^2)#
#Let " "u = ((x^2 + 1), v = (5x^4 + 2x + 9)#
#(du)/(dx) = (d/(dx)) (x^2 + 1) = 2x#
#(dv) / (dx) = d/(dx) (5x^4 + 2x + 9) = 20x^3 + 2#
#f'(x) = v (du)/(dx) + u (dv)/(dx)#
#f'(x) = (5x^4 + 2x + 9) * 2x + (x^2 + 1) * (20x^3 + 2)#
#=> 10x^5 + 4x^2 + 18x + 20x^5 + 2x^2 + 20x^3 + 2#
#color(brown)(=> 30x^5 + 20x^3 + 6x^2 + 18x + 2#