Question

y=(X-5)^3 * (X+4)^2
Найдите производную, не раскривая скобки

Answer 1

Ответ:

$y = (x - 5) {}^{3} (x + 4) {}^{2}$

$y '= ((x - 5) {}^{3} )' \times {(x + 4)}^{2} + ( {(x + 4)}^{2} )' \times {(x - 5)}^{3} = \\ = 3 {(x - 5)}^{2} {(x + 4)}^{2} + 2(x + 4) {(x - 5)}^{3} = \\ = {(x - 5)}^{2} (x + 4)(3(x + 4) + 2(x - 5)) = \\ = {(x - 5)}^{2} (x + 4)(3x + 12 + 2x - 10) = \\ = {(x - 5)}^{2} (x + 4)(5x + 2)$