Verified answer

[ f(x+Δx) - f(x) ] / Δx

[ (2 - 3 (x + Δx)^2 ) - (2 - 3x^2) ] / Δx

[ (2 - 3 (x^2 + 2x Δx + (Δx)^2 ) - (2 - 3x^2) ] / Δx

[ (2 - 3x^2 - 6x Δx - 3(Δx)^2 - 2 + 3x^2 ] / Δx

[ - 6x Δx - 3(Δx)^2 ] / Δx

- 6x- 3Δx. . . . .Δx--->0

- 6x- 3*0

-6x

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free to e-mail if have a question

Do you have to show it longhand according to the definition?

Or can you just use the power rule?

f'(x) = -6x

power rule w/ lim applied