If you change the x-axis to be roughly the same range as on graph.tk, it turns out like this:

http://www.wolframalpha.com/input/?i=d%2Fdx%28sin%28x*x%29+%...

This is actually a browser issue. AFAIK, Chrome and Firefox both round subpixels (e.g. 1.6px -> 2px). If you try doing the same thing in Safari you will notice that the graph looks as smooth as butter.

http://i.imgur.com/XzDgKtP.png

The graph.tk graph is displaying from ~-300 to ~300 while the WolframAlpha graph is only displaying from -10 to 10. That is hardly a fair comparison.

That's probably because the author is able to devote less resources per client than Wolfram?