If you mean,
(3x^2)(e^(6x-10x-3)) + (6x)(e^(3x^2-5x^2-3x+6-52))
3x^2 e^(6x-10x-3) + 6x e^(3x^2-5x^2-3x+6-52)
(which both say the same whereas your version opens more brackets than it closes - latex would reject it - did it?)
... then, re-read this bit...
(... by the derivative of the power.)you'll have as your derivative e to that same (complicated) power but the whole thing then multiplied ...
By the way, why not collect like terms in the power (and its deriv.) - but this is by the way.