using the product rule, differentiate and simplify: a) y=x(2x+1)^2 and b) y=x^2(3x-1)^2?

a)
y' = x d/dx (2x+1)^2+ (2x+1)^2 d/dx (x)
y' = x (2)(2x+1) d/dx (2x+1) + (2x+1)^2 (1)
y' = 2x(2x+1)(2) + (2x+1)^2
y' = 4x(2x+1)+(2x+1)^2
y' = (2x+1) ( 4x + 2x+1)
y' = (2x+1)(6x+1)
y' = 12x^2+8x+1

b)
y= x^2 (3x-1)^2
y' = x^2 d/dx ((3x-1)^2) + (3x-1)^2 d/dx (x^2)
y' = x^2 (2)(3x-1) d/dx ((3x-1)) + (3x-1)^2 (2x)
y' = x^2 (2)(3x-1) (3) + (3x-1)^2 (2x)
y' = 6x^2(3x-1) + 2x(3x-1)^2
y' = 2x(3x-1) (3x+3x-1)
y' = 2x(3x-1)(6x-1)
y' = 2x(18x^2-9x+1)
y' = 36x^3-18x^2+2x

y = x(2x + 1)^2
dy/dx = 1(2x + 1)^2 + x * 2(2x + 1) * 2
dy/dx = (2x + 1)^2 + 4x(2x + 1)

y = x^2(3x - 1)^2
dy/dx = 2x(3x - 1)^2 + x^2 * 2(3x - 1) * 3
dy/dx = 2x(3x - 1)^2 + 6x^2(3x - 1)