@aayush feynmann trick is not out of jee syllabus it's in every book resonance module Amit m Agarwal.
Yeah but it's not directly given, only used in some examples , also it's given as a property of definite integrals that we can partially differentiate both side wrt a parameter
jee syllabus (adv) contains differentiating under integral sign. but feynmann is extended version. like taking variable and thinking where to take variable.