Question

y=(x-10)^2e в степени х-6 как найти производную ?

Answer 1

$y = (x - 10)^2e^{x - 6} = (x^2 - 20x + 100)e^{x - 6}\\\\ \left[ \ (uv)' = u'v + uv' \ \right] \\\\ y' = ((x^2 - 20x + 100)e^{x - 6})' =\\\\= (x^2 - 20x + 100)'e^{x - 6} + (x^2 - 20x + 100)(e^{x - 6})' =$

$= (2x - 20)e^{x - 6} + (x^2 - 20x + 100)e^{x - 6} =\\\\= (x^2 - 20x + 2x + 100 - 20)e^{x - 6} = \boxed{(x^2 - 18x + 80)e^{x - 6}}$