Tiêu đề 250+ CÔNG THỨC GIẢI NHANH TOÁN 12 (chương trình mới).pdf ✅

250+ Cong thuc giid nhanh Toan 12 CHU DE i. n~o HAM v A KHAo sAT HAM so 1. D~o ham • Bii11g i/90 ham cua ml)t sa ham sa Sil clip co· biin va ham h9p D~o ham cua ham s6 sO' c~p D~o ham cua ham hqp cO' ban thucmg g~p (O' day u = u(x)) ( X11 )' = n . xn-l ( 11 )' 11-I I u =n·u ·u (~ x J =-~ x- UJ =-,~: (Fx)' = - 1 2/; (Fu)' = __!!__ 2Fu ( sinx )' = cosx (" smu )' = I ll ·COSU ( cosx )' = -sinx ( )' I • cosu = -u ·smu ... . , 1 , (tan x) =-2 cos - x (tanu)' =~ cos u (cot x )' =-+ I (cotu)' =-+ sm x sm u (ex)'= ex I ( e" )' = u' · e" (ax)' =ax ·In a I (a")' = u' · a1' · In a . 1 I ( )' u (Inx)' =- Inu =- . x u I 1 I (Ioga x ) =-· - (Ioga u )' = _u_ xlna ulna 3 250+ Cong thuc giid nhanh Toan 12 CHU DE i. n~o HAM v A KHAo sAT HAM so 1. D~o ham • Bii11g i/90 ham cua ml)t sa ham sa Sil clip co· biin va ham h9p D~o ham cua ham s6 sO' c~p D~o ham cua ham hqp cO' ban thucmg g~p (O' day u = u(x)) ( X11 )' = n . xn-l ( 11 )' 11-I I u =n·u ·u (~ x J =-~ x- UJ =-,~: (Fx)' = - 1 2/; (Fu)' = __!!__ 2Fu ( sinx )' = cosx (" smu )' = I ll ·COSU ( cosx )' = -sinx ( )' I • cosu = -u ·smu ... . , 1 , (tan x) =-2 cos - x (tanu)' =~ cos u (cot x )' =-+ I (cotu)' =-+ sm x sm u (ex)'= ex I ( e" )' = u' · e" (ax)' =ax ·In a I (a")' = u' · a1' · In a . 1 I ( )' u (Inx)' =- Inu =- . x u I 1 I (Ioga x ) =-· - (Ioga u )' = _u_ xlna ulna 3
250+ Cong thii'c giai 11hanh Toan 12 • Quy the tfnh ilfJO hiwt Cho u=u(x), v=v(x) la de ham s6 c6 d(,lo ham t~i di~m x thu(>c khoclng xac d!nh va C la h~ng s6. Ta c6: D~o ham cua ham h~ng I ! (c)' = o D~o ham ciia tBng, hi~u ( Zl + lJ )' = lf I + V1 ( u -v )' = u' - v' I ( u · v )' = u' · v + v' · u D~o barn cua tich =>(C·u)' =C.u' I I I ( ~} = "" 7' ·" ( v = v( x) * 0) D~o ham cua thuO'ng - - => ( c} C-u' ( ) - =--z- u=u(x)*O u u N ~u y = f (u), u = u ( x) D~o barn cua ham hqp => Y.: = y;, . u: • Co11g tlrfrc ti11h uha11h ily = -- cx+d cx+d ad-be (ex+ d) 2 ' ax2 + bx + c , ( ax 1 + bx + c J' •y= =>y= mx + n mx + n 4 amx.1 + 2anx + bn - cm (mx+n) 2 250+ Cong thii'c giai 11hanh Toan 12 • Quy the tfnh ilfJO hiwt Cho u=u(x), v=v(x) la de ham s6 c6 d(,lo ham t~i di~m x thu(>c khoclng xac d!nh va C la h~ng s6. Ta c6: D~o ham cua ham h~ng I ! (c)' = o D~o ham ciia tBng, hi~u ( Zl + lJ )' = lf I + V1 ( u -v )' = u' - v' I ( u · v )' = u' · v + v' · u D~o barn cua tich =>(C·u)' =C.u' I I I ( ~} = "" 7' ·" ( v = v( x) * 0) D~o ham cua thuO'ng - - => ( c} C-u' ( ) - =--z- u=u(x)*O u u N ~u y = f (u), u = u ( x) D~o barn cua ham hqp => Y.: = y;, . u: • Co11g tlrfrc ti11h uha11h ily = -- cx+d cx+d ad-be (ex+ d) 2 ' ax2 + bx + c , ( ax 1 + bx + c J' •y= =>y= mx + n mx + n 4 amx.1 + 2anx + bn - cm (mx+n) 2
250+ Cong thlrc giai nhanh Toan 12 2. Tinh do·n di~u cua ham stl • Tinlt i!o·n ili~u cua ham sB Gia su ham s6 y = f ( x) c6 d?o ham tren K c JR , trong d6 K la m<)t khoang, m<)t do?n ho?c nua khoang . • N~u f'(x) '?_ 0, '\Ix EK va /' ( x) = 0 chi t?i m<)t s6 hfru h?n diSm cua K thi ham s6 y = f(x) a6ng hdn tren K. • NSu f'(x)~O,'VxEK va /'(x)=O chit?im<)tsfJhfruh?ndiSmcua K thi ham s6 y = f (x) nghfch bi~n tren K. • NSu f'(x) = 0, '\Ix EK thi ham s6 y = f(x) kh6ng d6i tren K . • Cac buo·c aJ tim klwiing dBng biin, nghjch bi~n cua ham sa fix) ./ Buoc 1. Tim t~p xac djnh cua ham s6 . ./ Buoc 2. Tinh d?o ham f' ( x) . Tim cac di Sm -\ ( i = 1, 2, ... , n) ma t?i d6 helm s6 c6 d?o ham b~ng 0 ho?c khong t6n t?i . ./ Buoc 3. S~p x6p cac diSm -\ theo thl'.r hJ tang db va l~p bang bi6n thien cua f ( x) ho?c bang xet d~u cua .f' ( x) . ./ Bu6'c 4. KSt lu~n khoang d6ng bi6n, nghjch bi6n cua ham s6. <:s. Chu y: Ta ding c6 thS nh~n bi~t tinh don di~u cua ham s6 b~ng each quan sat hinh dang cua d6 thj di len (ham s6 d6ng bi~n) ho?c di xu6ng (helm s6 nghjch biSn). 3. ClJ'C tr! ciia ham stl Cho ham s6 y = f ( x) lien t\1c tren t~p K c JR, trong d6 K Ia m<)t khoang, m<)t do?n ho?c nua khoang va Xo E K . 5 250+ Cong thlrc giai nhanh Toan 12 2. Tinh do·n di~u cua ham stl • Tinlt i!o·n ili~u cua ham sB Gia su ham s6 y = f ( x) c6 d?o ham tren K c JR , trong d6 K la m<)t khoang, m<)t do?n ho?c nua khoang . • N~u f'(x) '?_ 0, '\Ix EK va /' ( x) = 0 chi t?i m<)t s6 hfru h?n diSm cua K thi ham s6 y = f(x) a6ng hdn tren K. • NSu f'(x)~O,'VxEK va /'(x)=O chit?im<)tsfJhfruh?ndiSmcua K thi ham s6 y = f (x) nghfch bi~n tren K. • NSu f'(x) = 0, '\Ix EK thi ham s6 y = f(x) kh6ng d6i tren K . • Cac buo·c aJ tim klwiing dBng biin, nghjch bi~n cua ham sa fix) ./ Buoc 1. Tim t~p xac djnh cua ham s6 . ./ Buoc 2. Tinh d?o ham f' ( x) . Tim cac di Sm -\ ( i = 1, 2, ... , n) ma t?i d6 helm s6 c6 d?o ham b~ng 0 ho?c khong t6n t?i . ./ Buoc 3. S~p x6p cac diSm -\ theo thl'.r hJ tang db va l~p bang bi6n thien cua f ( x) ho?c bang xet d~u cua .f' ( x) . ./ Bu6'c 4. KSt lu~n khoang d6ng bi6n, nghjch bi6n cua ham s6. <:s. Chu y: Ta ding c6 thS nh~n bi~t tinh don di~u cua ham s6 b~ng each quan sat hinh dang cua d6 thj di len (ham s6 d6ng bi~n) ho?c di xu6ng (helm s6 nghjch biSn). 3. ClJ'C tr! ciia ham stl Cho ham s6 y = f ( x) lien t\1c tren t~p K c JR, trong d6 K Ia m<)t khoang, m<)t do?n ho?c nua khoang va Xo E K . 5
250+ Cong thuc giai nhanh Toan 12 ·Ham s6 y = f (x) de.it qrc tri tc.ii diem x = x0 khi ham s6 y = f (x) lien tvc t(.li di~m X0 Va f' ( X) df>i d§u tlr ducmg sang am ho~c tlr am sang duong . • N~u f'(x) d6i d~u tlr dumig sang am khi qua di~m Xo thi Xo la di~m ci;rc de.ii cua ham s6 . • NSu f' (x) d6i dftu tlr am sang dzrong khi qua di~m Xo thi Xo la diem qrc ti@u cua ham s6. • f ( X 0 ) duqc gQi la gia tri C\fC d(.li (gia tri ClJC tieu) CUa ham s6 ky hi~U j~EJUcr), con di~m M(xo;f(xo)) duqc g9i la di@m qrc de.ii (diem ci;rc ti~u) cua d6 thi ham s6. 6 Di2m eve dc,.i cua d6 t~ ham s6 cua ham s6 Yer.. Gia tri <\>< ~~"(cue tiJu) J I cua ham so Dibn qrc tj2u cua ham s8 DiJm ct.re ti~u cua d6 thi ham s6 250+ Cong thuc giai nhanh Toan 12 ·Ham s6 y = f (x) de.it qrc tri tc.ii diem x = x0 khi ham s6 y = f (x) lien tvc t(.li di~m X0 Va f' ( X) df>i d§u tlr ducmg sang am ho~c tlr am sang duong . • N~u f'(x) d6i d~u tlr dumig sang am khi qua di~m Xo thi Xo la di~m ci;rc de.ii cua ham s6 . • NSu f' (x) d6i dftu tlr am sang dzrong khi qua di~m Xo thi Xo la diem qrc ti@u cua ham s6. • f ( X 0 ) duqc gQi la gia tri C\fC d(.li (gia tri ClJC tieu) CUa ham s6 ky hi~U j~EJUcr), con di~m M(xo;f(xo)) duqc g9i la di@m qrc de.ii (diem ci;rc ti~u) cua d6 thi ham s6. 6 Di2m eve dc,.i cua d6 t~ ham s6 cua ham s6 Yer.. Gia tri <\>< ~~"(cue tiJu) J I cua ham so Dibn qrc tj2u cua ham s8 DiJm ct.re ti~u cua d6 thi ham s6