Gilson Wurz

Polinômios a 1 ) G ( r ) = 5 2r 2 - 2 r - 1 dG ( r ) dr = dG ( r ) du du dr u = 2r 2 - 2 r - 1 du dr = ( 2r 2 - 2 ) ' ( r - 1 ) - ( 2r 2 - 2 ) ( r - 1 ) ' ( r - 1 ) 2 du dr = 4r ( r - 1 ) - ( 2r 2 - 2 ) ( r - 1 ) 2 = 4r 2 - 4r - 2r 2 + 2 ( r - 1 ) 2 = 2r 2 - 4r + 2 ( r - 1 ) 2 = 2 ( r 2 - 2r + 1 ) ( r 2 - 2r + 1 ) = 2 dG du = d du ( u 1/5 ) = 1 5 u 1 5 - 5 5 = 1 5 u -4/5 = 1 5u 4/5 = 1 5 5 u 4 dG ( r ) du = 2 5 1 5 ( 2r 2 - 2 r - 1 ) 4 , com r ≠ 1 ou ainda considerando os produtos notáveis , de tal modo que : 2r 2 - 2 = 2 ( r 2 - 1 ) = 2 ( r + 1 ) ( r - 1 ) u ( r ) = 2r 2 - 2 r - 1 = 2 ( r + 1 ) ( r - 1 ) ( r - 1 ) = 2 ( r + 1 ) du dr = 2 G ( u ) = 5 u dG du = 1 5u 4/5 = 1 5 5 u 4 dG dr = dG du du dr → dG dr = 1 5 5 u 4 · 2 = 2 5 · 1 5 [ 2 ( r + 1 ) ] 4 2 ) M ( x ) = x + x + x M ( x ) = ( x + ( x + x 1/2 ) 1/2 ) 1/2 dM dx = 1 2 ( x + ( x + x 1/2 ) 1/2 ) 1/2 d dx ( x + x + x ) dM dx = 1 2 x + x + x ( 1 + 1 2 x + x + 1