Find the rate of change at a point on a polynomial
Mathematica, 6 bytes
#'@#2&amp;

(Beat THAT, MATL and 05AB1E)
The first argument must be a polynomial, with # as its variable and with &amp; at the end (i.e. a pure function polynomial; e.g. 3 #^2 + # - 7 &amp;). The second argument is the x-coordinate of the point of interest.
Explanation
#'

Take the derivative of the first argument (1 is implied).
... @#2&amp;

Plug in the second argument.
Usage
#'@#2&amp;[4 #^3 - 2 #^4 + 5 #^10 &amp;, 19] (* The first test case *)


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