f(x) = (x^2 + 3x -2)^2
Let us calculate f'(x)
f'(x) = 2(x^2 + 3x -2) *(2x + 3)
= (2x^2 + 6x -4 )(2x + 3)
f'(1) = (2 + 6 -4)(2 +3)
= 4*5 = 20
==> f'(1) = 20
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