Google has added a bunch of examples to the potentialAction.mathExpression-input section of the Math Solver help documentation. These examples explain how to handle derivatives, integrals, and limits in that field.
You can see the examples over here - here is a screenshot, the previous version only had a few sentences for that whole section.
It reads now, "A placeholder for a mathematical expression (for example: x^2-3x=0) that is sent by Google to your website. You can then "solve" the math expression, which may involve simplifying, transforming, or solving for a specific variable. The string can take many formats (for example: LaTeX, Ascii-Math, or mathematical expressions that you can write with a keyboard). mathExpression-input is an annotated property. See the Potential Actions page for more information. For some problem types, the math_expression_string indicates both the problem type and parameters of the problem type. Here are some examples of the more complicated problem types so that you can anticipate and parse them correctly."
It then lists out the derivatives, integrals, and limits examples (click to enlarge):
So those who do math type of content, check out these examples.
Forum discussion at Twitter.