Your function can be written as the sum of two functions, let's say #f(x)# and #g(x)#
#y = f(x) + g(x)#
where #f(x) = (10-2x)(6-2x) * x# and #g(x) = x^3#.
This means that the derivative of #y# will take the form
#d/dx(y) = d/dx(f(x)) + d/dx(g(x))#
Now, you can differentiate #f(x)#, which can be written as the product of three other functions, by using the product rule.
For a function #f(x)# that can be written as
#f(x) = h(x) * i(x) * k(x)#
you can find its derivative by using the formula
#color(blue)(d/dx(f(x)) = [d/dx(h(x))] * i(x) * k(x) + h(x) * [d/dx(i(x))] * k(x) + h(x) * i(x) * [d/dx(k(x))])#
In your case, you have
#d/dx(f(x)) = [d/dx(10-2x)] * (6-2x) * x + (10-2x) * [d/dx(6-2x)] * x + (10-2x) * (6-2x) * d/dx(x)#
#f^' = (-2) * (6-2x) * x + (10-2x) * (-2) * x + (10-2x) * (6-2x) * 1#
#f^' = -12x + 4x^2 -20x + 4x^2 + 60 - 32x + 4x^2#
#f^' = 12x^2 -64x + 60#
Your target derivative will thus be
#y^' = 12x^2 - 64x + 60 + d/dx(3x^2)#
#y^' = 12x^2 - 64x + 60 + 3x^2#
#y^' = color(green)(15x^2 - 64x + 60)#
