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I then got this from it:

m = ((((x + h)^2) + (3*(x + h)) + 6) - (x^2 + 3x + 6)) / ((x + h) - x)

Which I eventually simplified to 2x + h^2 + 3h

And then: limit h -> 0: 2x + h^2 + 3h = 2x

So f ' (x) = 2x

Is that right? By doing this, I ended up getting a tangent line gradient of 19 (for x value of 8).

The reason I keep thinking this is wrong is because I thought f(x) = x^2 also ended up with f ' (x) = 2x