Unidad II: La derivada de una función. Objetivos particulares Al
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= ! ∆ = − ∆ ∆ = = = = − ∆ = − ∆ = ∆ ∆ = = = − ∆ = − ∆ =− ∆ ! ∆ = $ % ∆ = = $ #% " " − % +∆ #− $ # = $ #− $ #% & = +∆ & ∆ = ∆ % " " # = = ( = ( + −' ) ∆ & ∆ ∆ * + ∆ % , ∆ = − ∆ = (− ∆ = ( ! $ # = $ # = + − ' = −(% $ # = −( $ # = $ (# = $ (# + $ (# − ' ( = + −' =− ∆ = $ #− $ # =− = - , ∆ = ∆ . ! ( − $−(# ∴∆ = = (∴ ∆ = ( ∆ / + = ( 0 + ! " −' 1 + ∆ = $ + ∆ #( + $ + ∆ # − ' , % ∆ = $ + ∆ #( + $ + ∆ # − ' − , ! & 2 3 " − +' % ∆ =( ∆ +∆ *! ( ( + ∆ ! = & ∆ = (% & ∆ = ($ #$ (# + $ (# ( + $ (# ∆ = , / ∆ + + ∴∆ = ∆ % ∆ ∆ =( +∆ + ∆ *! " ! ∆ % , & ∆ = ($ # + ( + ∆ ∆ =(+ (+ ∴ = ( ∆ 4 2 ) / ! / / ! % ! ! . , " ∆ % ∆ ∆ → , ∆ = ∆ ∆ + ∆ $ → +∆ #− $ # ∆ ! , ! ! + * . " % " = $ # +∆ = $ +∆ # ! ∆ = $ +∆ #− $ # ∆ / ∆ = ∆ 4 ∆ → $ +∆ #− $ # ∆ %&! ∆ → 4 & ∆ = ∆ ∆ → 5 + $ +∆ #− $ # ∆ " = $ # , 2 ! 3 ! % ! ! =( " + ( −' − 1 + ∆ = ($ + ∆ # + $ + ∆ # ( − '$ + ∆ # − 6 ∆ = ($ + ( ∆ + ∆ = −' − '∆ − − ( ∆ = ( ∆ + ∆ ( + (∆ ∆ 8 ∆ ∆ = ∆ → ∴ *! " $ → ( ∆ → ( + − + ∆ & 7 ∆ → ∆ + (∆ + −' ∆ = (+ ∆ + ( +∆ #+ $ ( ( +' + ∆ + ∆ ∆ ∆ ( +( ∆ +∆ # ( − '∆ + ∆ − '# −' ! " ( = " +∆ = 6 ∆ = , ! ∆ = ∆ = $ + ∆ #( $ +∆ #− $ + ∆ #( − $ +∆ #− $ + ∆ #( $ − # − ( [ $ + ∆ # − [ $ + ∆ # − ]$ − # − ∆ = ( ( + ( − ( − ] ∆ −( ∆ + ∆ −∆ − [ $ + ∆ # − ]$ − # ( ∆ −( ∆ + ∆ −∆ [ $ + ∆ # − ]$ − # ( ( ( − ( ∆ + ( ∆ & 7 ∆ → ∆ → ∆ = ∆ → ∆ [ = −( + ∆ −∆ $ + ∆ # − ]$ − # ( −( $ − #( ( ! " #7 " = ( + ∆ & −'% ∆ ∆ = + = ' ∆ ∆ =( − % & ! = (+ % & ! ( = % & ! ∆ & (# ) # # # ∆ % ∆ ( = #, ' # 7 # 7 # 7 + ( ) % ! # # = = # = # = '# = 9# = # − ( ( −' − −9 − +( ( − ( ( − ( + = − , + 5 ! %