Help me please help me please help me

Question

Find the derivative of y=x³+1/x²+3(x²-2x^-1+1)

Answer 1

y = x^3+1/x^2 +3(x^2-2x^-1 +1)

may be a little ambiguous,

but as written it's

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

then

y' = 3x^2 - 1/x^3 + 6x +6/x^2

but you may have left out some parentheses which would change the answer, and make the derivative more complicated. You might have meant y= (x^3+1)/(x^2+3)(x^2-2x^-1 +1) or another expression with some similar parentheses, such as y=(x^3+1)/[x^2 +3(x^2-2x^-1+1)] or y= (x^3+1)/x^2 +3(x^2-2x^-1+1)That would make the problem complicated and tedious in solving for a derivative. It this is a "precalculus" question, odds are they gave you the easier, first version, solved above for y'

the last version though is also easy.

y = (x^3+1)/x + 3(x^2 -2x^-1 +1)

= x^2 + 1/x + 3x^2 -6x^-1 +3

= 4x^2 -5x^-1 + 3

y' = 8x +5/x^2

It also has the most simple solution. It might be the way the problem was intended, although it's a little strange to write (x^3+1)/x when they could have just put x^2 + 1/x