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Problem Seed:

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For each example below, list the label of the differentiation rule used in that example:

  ? Sum Rule Product Rule Chain rule Quotient rule  1. $(f(x) - g(x) )' = f'(x) - g'(x)$

  ? Sum Rule Product Rule Chain rule Quotient rule  2. $( f(g(x)) )' = f'(g(x))g'(x)$

  ? Sum Rule Product Rule Chain rule Quotient rule  3. $(f(x) + g(x) )' = f'(x) + g'(x)$

  ? Sum Rule Product Rule Chain rule Quotient rule  4. $( f(x)g(x) )' = f'(x)g(x) + f(x)g'(x)$

  ? Sum Rule Product Rule Chain rule Quotient rule  5. $\frac{d}{dx} \sin(\cos(x)) = - \cos(\cos(x))\sin(x)$

You can view the source for this problem. or consult the documentation for more details on the PG language.

There are only a few examples in this problem. A production verison would need more examples to choose from.