That is called implicit differentiation. You would need to use chain rule and product rule (mostly).
But for this problem (Quadratic equation), you can write:
Y = [-A ± √(A^{2} + 4BX)]/2
and carry-out straight-forward differentiation.
“... mathematics is only the art of saying the same thing in different words” - B. Russell
Subhotosh, many thanks.
Lazar
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