The difference quotation of the function given will be 4x+2h-1.
(x) = 2x²-x-1
Using this function, plug everything into the difference quotient formula
[2(x+h)²-(x+h)-1-(2x2-x-1)]/h
[2(x²+2xh+h²)-x-h-1-2x²+x+1]/h
Distribute the last set of parenthesis from the foiled part
[2x²+4xh+2h²-x-h-1-2x²+x+1]/h
Simplify by combining like terms
[4xh+2h²-h]/
Factor an h from the numerator
[h(4x+2h-1)]/h
cancel out the h's
4x+2h-1
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