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NOMBRE DEL TRABAJO:
EJERCICIOS DE CALCULO CORRESPONDIENTES AL LIBRO DE WILLIAM ANTHONY GRANVILLE
NOMBRE DEL PROFESOR:
M.C RAMON SALVADOR SOLER HERNANDEZ
GRUPO:
2DO A
MATERIA:
CALCULO DIFERENCIAL E INTAGRAL
CUATRIMESTRE:
2DO CUATRIMESTRE
TURNO:
MATUTINO
EDIFICIO:
1 AULA NO 9 PLANTA BAJA
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TEMA 1
DERIVACION
DE
FUNCIONES
ALGEBRAICAS
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5 4 4
1) =
2) = 4a
3) Y= +5=
4) - 8 =
+8
5) y= · 2x = 10x
6) y= =
7) y= =
Y= =
Y= 3 ( =
Y= 3 =
Y= 3
Y=
8) y= = =
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Y=
9) )= =
10)
Y=
11)
12)
13)
14)
= =
16)
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-
15) -
39.-
40.-
41.-
42.-
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46.- =
=
47.-
48.- =
49.-
50.-
Y
51.-
52.-
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53.-
52.-
53.-
54.-
55.-
56.-
57.-
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58.-
59.-
43.-
Δy=
Δy=
44.- g=
Δy= =
Δy= -
Δy=
45.-
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=
=
= -
46.-
47.-
=
=
60.- y= 3 ; x=3
= 3 · -2x = -6x = =
= -18 = -450
61.- y= ; x=2
y
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=
62.- y= ;
= = =
= = =
63.- Y = X ; x=3
= =
= + = = = 9
64.- Y= ; x=2
= ·
dy= = =
= =
=
= =
= =
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PROBLEMA 52 PAG 46
PROBLEMA 65 PAG 46
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PROBLEMA 25 PAG 44
48)
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Derivadas de Funciones trascendentales
1.
2.
3.
4.
5.
Propiedades
1.
2.
3.
4.
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Problema 19 pag. 44
R=
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Problema 33 pag. 45
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Problema 29 pág. 45
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Problema 28 Pág. 45.
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31.
=
= = =
32.
=
=
33.
= -
= -
= =
34.
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= =
35.
=
36.
37.
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40.
41.
42.
43.
44.
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Tema 2 DERIVADAS
DE
FUNCIONES
TRASCENDENTALES
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23.-
= =
24.-
=
25.-
. = .
. = =
26.-
=
=
28.- .
=
=
29.-
=
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30.- =
31. - = f(x)
32.-
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36.-
37.-
37.-
37.-
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38.-
39. –
40.-
41.-
42.- , x=4
43.-
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44.-
45.-
46.-
47.-
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54.-
55.-
56.-
57.-
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58.-
59.-
60.-
61.-
48.-
49.-
50.-
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51.-
52.-
53.-
54.-
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57._
*
=
.
=
59.-
Y’= =
60.-
Y’=
61.-
Y’= =
62.-
36.-
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14.- S = ln
S´ = [ • b - • -b] - [ + ]
S´ = [ ] - [ ] =
15.- f(x) = x² ln x²
f´(x) = [x² • • 2x + ln x² + • 2x] = [2x + ln x² • 2x] = 2x(1 + ln x²)
f´(x) = 2x (1 + 2 ln x) 16.- y = enx
y´ = enx • n = nenx
17.- y = 10nx
y´= nx(10)xn-1 •0 + ln 10.0nx • n 18.- y = ex²
= ex² • 2x = 2x ex²
19.- y =
y´ = [ ] = =
20.- S =
S´= • =
21.- Z = b2y
= b2y ln b • (2y) Z´ = 2b2y ln b 22.- U = Ses
U´ = S • d ( )
U´ = S • es • 1 = u´= es (S+1)
28. - - ) = )
= [ . ( + ) + . 0] = ( )
In y= in + in - =
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= ( - ) [ . ( + . ) ] = ( )
29. - y= =
=[ ] = =
In y= in - - in + = . ( ) - . ( )
In y=
= . =
30. - s= = =
= ] = =
31-. F (x) = in (x) =
(x) = . [
(x) = .
(x) = . = .
(x) =
32. - y= =
= x + . In x .1= + in x= (1+in x)
In y = x in x = [x. + in x .1] = = (1 + in x)
33.- y= =
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= + in x = + =
In y= in x = [ . + In x. ] = [ + ]
= [ ] = ( )
34. - s= ( = ( (in -1)
In s= t in = [t. [ ] + in . 1] = ( (-1 + in )
= t ( . [ ] + ( in . 1 = - ( ) ( + ( in
= ( (-1 + in )
35.- y= = y [ + - ]
In y= in x + in 3x+a - in 2x+b
In y= + . . 3 - . . 2 = = y [ + - ]
1.- Y= in (a x + b)
= . = . a =
2.- Y= in (a + b)
= . 2ax =
3.- y= in (ax + b
= 2 in (ax + b)
= 2. . a =
4. - y= in a
= n . In ax = n [ . a] + in ax . O
= =
5. - y= in
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= 3 in x = 3 . . 1 =
6. - y= I x [(In x ]
3 (in x . d (in x) = 3 (in x . =
7. - y= in n (2 - 3 + 4)
= . 6 - 6x = =
8. - y= log
= . [