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FORMULARIO

DERIVADAS:Sea la funcn: Su derivada es :

f(x) =K f '(x) = 0

f(x) =x f '(x) =1

f(x) =kg(x) f '(x) =kg '(x)

f(x) =xn f '(x)=nxn-1

F(x) = f(x)+g(x)h(x) f'(x) = f '(x)+g '(x)h '(x)

f(x) =[g(x)]n f '(x)=n [g(x)]n-1g '(x)

F(x) = f(x)g(x) F(x) = f(x)g '(x)+g(x) f '(x)

F(x) =f(x)

g(x)=

u

vF '(x)=

g(x) f '(x) f(x)g '(x)

[g(x)]2g(x) 0

Sea u= g(x)

f(x) = sen(u) f '(x) = c!s(u)u '

f(x) = c!s(u) f '(x) = sen(u)u '

f(x) = "an(u) f '(x) = sec2(u)u '

f(x) = c!"(u) f '(x) = csc2(u)u '

f(x) = sec(u) f '(x) = sec(u)"an(u)u '

f(x) = csc(u) f '(x) = csc(u)c!"(u)u '

f(x) = au f '(x)= au ln(a)u '

f(x) = eu f '(x) = eu u '

f(x) = l!ga(u) f '(x) =1

(u)ln(a)u '

f(x) = ln(u) f '(x) =1

uu '

f(x) =uv f'(x) = v uv1u '+uln(u)v '

ngulos negativos:sin(-x) # $sin(x) c!s(-x)# %c!s(x) "an(-x) # $sin(x)

Suma o diferencia de ngulos:sin (x y )=sin (x )cos(y)sin(y )cos (x)

cos (x y )=cos (x )cos(y )sin(y )sin (x )

L!mites im"ortantes:

limx 0

( sin (x )x )=1limx 0(1cos (x)

x )=limx 0 (cos(x )1

x )=0

IDE#$IDADES $RI%O#OM&$RI'ASRec!"rocas: (itag)ricas:

sin (x )csc (x )=1cos2 (x )+sin2(x)=1

( x )+1=sec2(x)cos ( x ) sec ( x)=1 tan2

(x )+1=csc2(x )tan (x ) cot (x )=1cot2

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ngulo do*le: 'ociente:sin (2x )=2sin (x )cos(x )

cos (2x )=cos2 (x )sin2 (x ) tan(2x)= 2tan(x)

1tan2(x)tan (x )=

sin (x )cos (x)

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cos (2x )=2sin2 ( x )1

cos (2x)=12cos2 (x )