How do you differentiate this problem?!

the answer should be 48x^3 + 48x^2 - 50x -21

I should expand the (2x+3)^2 and multiply (3x-2) and (x-1) like you said
(4x^2 + 12x + 9)(3x^2- 5x + 2)

Then multiply all of them together you will get
12x^4 + 16x^3 - 25x^2 - 21

Take derivative of it will be 48x^3 + 48x^2 - 50x -21

d/dx [(2x+3)² (3x−2) (x−1)]

= d/dx ((2x+3)²) * (3x−2) * (x−1)
+ (2x+3)² * d/dx (3x−2) * (x−1)
+ (2x+3)² * (3x−2) * d/dx (x−1)

= (2(2x+3) * 2) * (3x−2) (x−1) + (2x+3)² * 3 * (x−1) + (2x+3)² (3x−2) * 1

= 4 (2x+3) (3x−2) (x−1) + 3 (2x+3)² (x−1) + (2x+3)² (3x−2)

= (2x+3) [ 4 (3x−2) (x−1) + 3 (2x+3) (x−1) + (2x+3) (3x−2)]

= (2x+3) (12x² − 20x + 8 + 6x² + 3x − 9 + 6x² + 5x − 6)

= (2x+3) (24x² − 12x − 7)

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Alternatively, you could expand (3x−2) (x−1) before differentiating:

d/dx [(2x+3)² (3x−2) (x−1)]

= d/dx [(2x+3)² (3x² − 5x + 2)]

= d/dx ((2x+3)²) * (3x² − 5x + 2) + (2x+3)² * d/dx (3x² − 5x + 2)

= 2(2x+3)² * 2 * (3x² − 5x + 2) + (2x+3)² * (6x − 5)

= (2x+3)² [4 (3x² − 5x + 2) + (2x+3) (6x − 5)]

= (2x+3)² (12x² − 20x + 8 + 12x² + 8x − 15)

= (2x+3)² (24x² − 12x − 7)

Just by looking at it I can tell it will be long
I found 4(2x+3)(3x-2)(x-1) + 3(2x+3)^2 (x-1) + (2x+3)^2(x+1) before developing and simplifying I got

72x^3 + 98x^2 +58x - 75

Never mind I did derivatives

Even though It might take a while you could just multiply everything out first and not worry about product rule

(2x+3)^2 (3x-2)(x-1) = (2x+3)^2 (3x^2-5x+2)
and use the product rule

Do your own Homework
Good luck