Graphing Calculator
Drag to pan, scroll to zoom, hover to trace. The derivative is worked out symbolically from the parse tree, not estimated, so it comes back as an expression you can read.
+ − * / ^, parentheses, and sin cos tan asin acos atan sqrt abs
ln log exp floor ceil sign, with the constants pi and e. Juxtaposition
multiplies, so 2x and 3sin(x) both work.
Exact algebra comes from nerdamer (MIT), which is the one piece of this site I did not write. It is 426 kB, so it is fetched when you press the button and not before.
Adaptive Simpson, refined until the estimate stops moving. Signed, so area below the axis counts as negative.