Il Maraschini-Palma - volume 5

5 ESERCIZI Calcolo delle derivate PER ESERCITARSI CON GRADUALIT Scrivi la funzione derivata delle seguenti funzioni, utilizzando le derivate delle funzioni fondamentali e le proprietà della derivata rispetto alle operazioni aritmetiche. 1 143 y = __ + x x 1 1 __2 x] [ x2 + 1 144 y = ______ x2 x 145 y = _____ 1 + 1 _____ x 146 y = 1 + x 1 + x 2 + x 3 147 148 149 150 151 2 __ [ x3 ] x(x + 2) _______ 2] [ (x + 1) 2 x + 2x + 3 ___________ [ x4 x+2 y = _____ x 2 x3 + 3x + 1 y = __________ x 1 5 x___________ 2x3 3 y= x 1 y = _______ 2x2 + 1 3 x2 y = ______2 3+x 4 ______ [ (x 2)2 ] 3 [ (x 1)2 5 [ 164 y = 3x 2 + x + 1 2 x x 165 y = ______ 2x + 1 3 x2 ] ] x3 3x2 + 2 ________ [ (x2 2)2 ] 8(2x + 1) _____________ [ (4x2 + 4x 1)2 ] 5 _______ [ (x 1)2 ] x(x2 2) 2 __________ [ (x2 + x 1)2 ] 1 10 ________ [ (2x + 1)2 ] 2 1 x ________ [ (x2 + 1)2 ] x2(2x 3) _________ [ (x 1)2 ] 4 3 2 x 6x + x + 10 ________________ [ (x 3x + 2)2 ] 2 1 170 y = __2 + 3 + x x 3 x 2 ______ [ x3 ] 3x2 + 4x 3 171 y = _____________ 3x2 + 4x + 1 8(3x + 2) ______________ [ (3x + 1)2(x + 1)2 ] x + x3 172 y = ______ x+2 x3 + 3x2 + 1 2 ____________ [ (x + 2)2 ] 1 174 y = ____________ (2x + 1)(x 3) [ 4x + 2 _________ [ x2(x 1)2 ] x3 + 5x 169 y = __________ 2 x 3x + 2 12x ________ [ (3 + x2)3 ] 3 [ x2(x 4)2 ] x3 168 y = _____ 1 x x3 + 2x2 + 8 173 y = ___________ x2 4(x 2) ________ 2 x 4x + 8 __________ x2 x + 2 167 y = _________ x2 x 4x _________ [ (2x2 + 1)2 ] x 158 y = ______2 1+x x 4 159 y = _______ 4x + 1 x2 160 y = ______ x2 + 9 x2 + 9 161 y = ______ x2 x 2 162 y = _____ x2 x2 163 y = _____ x 1 ] 4x 4x + 3 ____________ 152 y = 4(x + 3 + x ) 1 156 y = (x2 x + 1) _________ 2 x +x 1 4x 3 157 y = ______ 2x + 1 2 2x 3x 4 ____________ 2 3x 153 y = ______ 2 x 2 2 154 y = ___________ 2 4x + 4x 1 5 155 y = _____ 1 x ] x 2 166 y = _______2 4x x 3 x 16 _______ [ ] x3 4x 5 _____________ [ (2x + 1)2(x 3)2 ] x + 4x 1 175 y = _______ x2 [ 1 y = _______4 1 2x x2 x 1 + 3 177 y = ___________ x x2 + 12 _______ x4 ] x3 8 _________ [ (2x4 1)2 ] 176 3 x 3x + 2 __________ [ x3 ] 1 ex + xex ___________ (1 + ex)2 ] x 178 y = ______x 1+e [ x e ________ 179 y = (1 ex) 1 [(e 1)2 ] x 1 + ex 180 y = ______x 1 e [(e 1)2 ] ex 181 y = __ x [ 2e ________ x x e (x 1) ________ x ] x2 15 ________ 1 182 y = ____ cosx [ cos2x ] x 18 ________ (x2 + 9)2] ] 183 y = xtanx [tanx + x + xtan2x] [ (4x 1)2 ] [ 18 ___ [ x3 ] 4 x _____ [ x3 ] x (x 2) _________ [ (x 1)2 ] senx _____ tanx 184 y = ____ x 1 tanx ______ ____ [ xcos2x senx 185 y = ________ 1 cosx 1 ________ [ cosx 1 ] senx 186 y = ____ x x3 6 ______ [ x3 ] 2x 187 y = _______ 1 + tanx 2x2 + 2x 1 ___________ [ (2x + 1)2 ] x + senx 188 y = _______ x senx x2 ] xcosx senx ___________ [ x2 ] 2 2(cos x + senxcosx x) ____________________ [ (cosx + senx)2 ] xcosx senx 2 ________________ [ x2 2xsenx + sen2x ] 297

Il Maraschini-Palma - volume 5
Il Maraschini-Palma - volume 5