Compare each line with the quotient rule. The parts in line 1 are shared and correct, so check the order of the subtraction in each numerator, then the arithmetic.
Working
u=2x+3,u′=2;v=x2+1,v′=2x
A1 and B1 are right.
(vu)′=v2u′v−uv′
The rule starts with the derivative of the top times the bottom. A2 writes uv′ − u′v, the negative of this, so A goes wrong at A2.
B4 is right. A3’s 3/2 is the same size with the opposite sign, as a reversed subtraction always gives.
f(1)=2.5,f(1.1)≈2.35
A check: f is falling near x = 1, so f′(1) must be negative.
Answer
B is right:f′(1)=−23
The answer is B is right: f prime of 1 is −3/2. A subtracts in the wrong order and gets the opposite sign..
Check
f(1) = 2.5 and f(1.01) ≈ 2.485, so f is falling at x = 1 and f′(1) must be negative, about −1.5.
Where this goes wrong
Writing the numerator of the quotient rule in the wrong order. Unlike the product rule, the order matters: u′v − uv′, the derivative of the top first. The reversed order gives the right size with the wrong sign, which is easy to miss without a check.