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Exercise:
textbfRinfresco sulle derivate Calcola la derivata algebrica delle seguenti funzioni yfx abcmulti abc yx^ abc y-fracx^+x abc ysqrtx+x+ abc ylnx-x^- abc y^x-e^x abc ysinx+cosx abc yx^log_x abc yx^+x^- abc ysin^x abc yfracx+x- abc yfracx^-x+x^-x+ abc yx^-x^^- abc ysin^sinx abc ysqrtx^- abc ylogx^+x abc yfrac+sqrtx-sqrtx abc yxe^/x abc yfracsqrtax-x^ abc ylnsqrt+^x abc yx^e^x^ abc yfractan^x abc ylnleftfrac+x-xright abc yx^x abc ysinhx abc yarcsinx abc yfracxlnx abcmulti

Solution:
abclist abc y'x^ abc y'-x^+ abc y'fracsqrtx+ abc y'fracx+x^- abc y'ln^x-e^x abc y'cosx-sinx abc y'xlog_x+x^fraclnxxleftlog_x+fraclnright abc y'xx^-+x^+xx^+x abc y'cos^xln^x abc y'frac x--x+ x-^frac-x-^ abc y'fracx-x^-x+-x^-x+x-x^-x+^frac-x^-x+x^-x+^ abc y'-x^-x x^-x^^-frac-x^+xx^-x^^ abc y'sinsinxcossinxcosx abc y'fracxsqrtx^-fracxsqrtx^-. abc y'fracln fracx+x^+x abc y'fracfracsqrtx -sqrtx-+sqrtx frac-sqrtx-sqrtx^fracsqrtx-sqrtx^ abc y'e^/x+xe^/xfrac-x^-fracxe^/x abc y'frac-a-x^sqrtax-x^^fracx^-asqrtax-x^^quad in quanto abbiamo usato che fracsqrtdotsdots^-/ abc y'fracsqrt+^x fracsqrt+^x ln ^xfracln^x+^x abc y'x^e^x^+x^e^x^x+x^x^e^x^ abc Per questo usiamo che la derivata di tan è -tan^ per ottenere y'frac-tan^x -tan^x fractan^x-tan^x abc y'fracfrac+x-x frac-x-+x--x^frac-x+x frac-x^frac-x^ abc Sfruttando il fatto di scrivere x^xe^lnx^xe^xlnx otteniamo: x^x'x^x xlnx'x^x lnx+x fracxx^x+lnx. abc ysinhxfrace^x-e^-ximplies y'frace^x+e^-xcoshx abc yarcsinximplies y'fraccosarcsinxfracsqrt-x^ abc yfracxlnximplies y'fraclnx-ln^x abclist
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Exercise:
textbfRinfresco sulle derivate Calcola la derivata algebrica delle seguenti funzioni yfx abcmulti abc yx^ abc y-fracx^+x abc ysqrtx+x+ abc ylnx-x^- abc y^x-e^x abc ysinx+cosx abc yx^log_x abc yx^+x^- abc ysin^x abc yfracx+x- abc yfracx^-x+x^-x+ abc yx^-x^^- abc ysin^sinx abc ysqrtx^- abc ylogx^+x abc yfrac+sqrtx-sqrtx abc yxe^/x abc yfracsqrtax-x^ abc ylnsqrt+^x abc yx^e^x^ abc yfractan^x abc ylnleftfrac+x-xright abc yx^x abc ysinhx abc yarcsinx abc yfracxlnx abcmulti

Solution:
abclist abc y'x^ abc y'-x^+ abc y'fracsqrtx+ abc y'fracx+x^- abc y'ln^x-e^x abc y'cosx-sinx abc y'xlog_x+x^fraclnxxleftlog_x+fraclnright abc y'xx^-+x^+xx^+x abc y'cos^xln^x abc y'frac x--x+ x-^frac-x-^ abc y'fracx-x^-x+-x^-x+x-x^-x+^frac-x^-x+x^-x+^ abc y'-x^-x x^-x^^-frac-x^+xx^-x^^ abc y'sinsinxcossinxcosx abc y'fracxsqrtx^-fracxsqrtx^-. abc y'fracln fracx+x^+x abc y'fracfracsqrtx -sqrtx-+sqrtx frac-sqrtx-sqrtx^fracsqrtx-sqrtx^ abc y'e^/x+xe^/xfrac-x^-fracxe^/x abc y'frac-a-x^sqrtax-x^^fracx^-asqrtax-x^^quad in quanto abbiamo usato che fracsqrtdotsdots^-/ abc y'fracsqrt+^x fracsqrt+^x ln ^xfracln^x+^x abc y'x^e^x^+x^e^x^x+x^x^e^x^ abc Per questo usiamo che la derivata di tan è -tan^ per ottenere y'frac-tan^x -tan^x fractan^x-tan^x abc y'fracfrac+x-x frac-x-+x--x^frac-x+x frac-x^frac-x^ abc Sfruttando il fatto di scrivere x^xe^lnx^xe^xlnx otteniamo: x^x'x^x xlnx'x^x lnx+x fracxx^x+lnx. abc ysinhxfrace^x-e^-ximplies y'frace^x+e^-xcoshx abc yarcsinximplies y'fraccosarcsinxfracsqrt-x^ abc yfracxlnximplies y'fraclnx-ln^x abclist
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Attributes & Decorations
Tags
Extra, Successioni e serie
Difficulty
(3, default)
Points
0 (default)
Language
ITA (Italiano)
Type
Calculative / Quantity
Decoration
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