Question

знайти похідну функції (х^2+х)(х^3-х)

Answer 1

Ответ:

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

$y '= ( {x}^{2} + x)'( {x}^{3} - x) + ( {x}^{3} - x)'(x {}^{2} + x) = \\ = (2x + 1)( {x}^{3} - x) + (3 {x}^{2} - 1) ( {x}^{2} + x) = \\ = 2 {x}^{4} - 2 {x}^{2} + {x}^{3} - x + 3 {x}^{4} + 3 {x}^{3} - {x}^{2} - x = \\ = 5 {x}^{4} + {x}^{3} - {x}^{2} - 2x$