Question

Помогите, не понимаю!
Найти y''' , если y=x*cosx^2

Answer 1

$y'=cos x^2+x(-sin x^2)*2x$

$y'=cos x^2-2x^2sin x^2$

$y''=-2xsin x^2-(4xsin x^2+2x^2cos x^2*2x)$

$y''=-2xsin x^2-4xsin x^2-4x^3cos x^2$

$y''=-6xsin x^2-4x^3cos x^2$

$y'''=-6sin x^2-6xcos x^2*2x-12x^2cos x^2-4x^3(-sin x^2)*2x$

$y'''=-6sin x^2-12x^2cos x^2-12x^2cos x^2+8x^4sin x^2$

$y'''=-6sin x^2-24x^2cos x^2+8x^4sin x^2$