I've tried part b, however, I do not know which step I did wrong and cannot prove part b. I want to ask how to do part b and c with steps? thank you

9. Let f(x) = (1+z?)-4. (a) Show that (1 + x) f'(x) + if(x) = 0. (b) Let n be a non-negative integer, show that (1 + 12) f(n+2)(x) + (2n +3)xf(n+1)(x) + (n + 1)? f()(x) = 0. term r. (c) Hence, or otherwise, find the Taylor series of (1 + z?) : at x = 0 up to the ( 1 + x " ) f (x ) + xtla ) = 0 fix) = CHAR) f'lx ) = - CHx) dan ( 1 +X" ) f' (x ) + _du do" x fix ) = - ( 1 + x " ) f(x ) - E cra dr don't filx ) = Cothe ( 1+x 3 )-d dx" t' (x ) + c" (1+23 dn- dx-7 f ( x ) dx- i f' (x ) Co (Itx2 ) fintz) ( x ) + c" ( 2 x ) fin+ ( x ) + ( 2 (2 ) fin) ( x ) ( 1+ x " ) fintz x ) + n( 2x ) font (x ) + "in -2 /{ (m) (x ) Air xfix ) = damn f(x ) danflx ) " ( x ) + n f ( ( x ) ( 1 +xx ) flute (x ) +1 ( 27 ) finty " ( x ) + 1( n- ) 2 2 (" ( x ) + x fint ( x ) tuf" ( x ) = 0 f ( x ) +