Exercise:
nprvmulticols abclist abc displaystyle fracddddx left sinx right abc displaystyle fracddddx left cosx right abc displaystyle fracddddx left sin^x right abc displaystyle fracddddx left cos^x right abc displaystyle fracddddx left sinx right abc displaystyle fracddddx left cosx right abc displaystyle fracddddx left sin^x right abc displaystyle fracddddx left cos^x right abc displaystyle fracddddx left x sinx right abc displaystyle fracddddx left x^ cosx right abc displaystyle fracddddx left x sin^x right abc displaystyle fracddddx left x cos^x right abc displaystyle fracddddx left sinx^ right abc displaystyle fracddddx left cosx^ right abc displaystyle fracddddx left sin^x^ right abc displaystyle fracddddx left cos^x^ right abc displaystyle fracddddx left sin^x^ + right abc displaystyle fracddddx left cos^x^ + x right abc displaystyle fracddddx left sinxcosx right abc displaystyle fracddddx left sin^xcosx right abc displaystyle fracddddx left x^ sin^x right abc displaystyle fracddddx left cos^x^ + right abc displaystyle fracddddx left sin^x^cos^x^ right abc displaystyle fracddddx left x sin^x^cosx right abclist nprvmulticols

Solution:
abclist abc fracddddx biglsinxbigr cosx abc fracddddx biglcosxbigr -sinx abc fracddddx biglsin^xbigr sinxcosx abc fracddddx biglcos^xbigr cos^x-sinx -cos^xsinx abc fracddddx biglsinxbigr cosx abc fracddddx biglcosxbigr -sinx abc fracddddx biglsin^xbigr sinx cosx sinxcosx abc fracddddx biglcos^xbigr cos^x-sinx -cos^xsinx abc fracddddx biglxsinxbigr sinx + xcosx abc fracddddx biglx^cosxbigr xcosx - x^sinx abc fracddddx biglxsin^xbigr sin^x + x sinxcosx abc fracddddx biglxcos^xbigr cos^x + x cos^x-sinx cos^x - xcos^xsinx abc fracddddx biglsinx^bigr cosx^ x abc fracddddx biglcosx^bigr -sinx^ x abc fracddddx biglsin^x^bigr sinx^cosx^ x xsinx^cosx^ abc fracddddx biglcos^x^bigr cosx^-sinx^ x^ -x^cosx^sinx^ abc fracddddx biglsin^x^+bigr sin^x^+cosx^+ x abc fracddddx biglcos^x^+xbigr cosx^+x-sinx^+xx+ -x+cosx^+xsinx^+x abc fracddddx biglsinxcosxbigr cos^x - sin^x abc fracddddx biglsin^xcosxbigr sinxcosxcosx + sin^x-sinx sinxcos^x - sin^x abc fracddddx biglx^sin^xbigr xsin^x + x^ sin^xcosx xsin^x + x^sin^xcosx abc fracddddx biglcos^x^+bigr cos^x^+-sinx^+ x -xcos^x^+sinx^+ abc fracddddx biglsin^x^cos^x^bigr biglsinx^cosx^ xbigrcos^x^ &quad + sin^x^biglcosx^-sinx^ xbigr xsinx^cosx^cos^x^ - xsin^x^cosx^sinx^ abc fracddddx biglxsin^x^cosxbigr sin^x^cosx &quad + xBiglsin^x^cosx^ xcosx + sin^x^-sinxBigr abclist