Question

differentiate y=(x+1)^2(x+2)^2

Answer 1

The derivative is:
\[2 (1+x)^2 (2+x)+2 (1+x) (2+x)^2 \]
Simplified:
\[2 \left(6+13 x+9 x^2+2 x^3\right) \]

Answer 2

i got the same answer as you but in the solutions it says its 2(x+1)(x+2)(2x-3). any clue?

Answer 3

The solution has a sign error:

2(x+1)(x+2)^2 + 2(x+1)^2(x+2) = 2(x+1)(x+2)(2x+3)
^^^ plus

Answer 4

the solution is just the factored form of what you got from above.
If you factor out a 2 and (x+1) and (x+2) you get
-> 2(x+1)(x+2)[(x+1) + (x+2)]
add inside brackets
->2(x+1)(x+2)(2x+3)