CD_U3_A4_FRPB
14
NOMBRE: FRANCISCO JAVIER PRIEGO BRITO FACILITADOR: OSCAR RICARDO DELFIN SANTIESTEBAN MATERIA: CÁLCULO DIFERENCIAL CARRERA: DESARROLLO DE SOFTWARE TEMA: DERIVACION DE FUNCIONES ALGEBRAICAS
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Transcript of CD_U3_A4_FRPB
NOMBRE: FRANCISCO JAVIER PRIEGO BRITO
FACILITADOR: OSCAR RICARDO DELFIN SANTIESTEBAN
MATERIA: CÁLCULO DIFERENCIAL
CARRERA: DESARROLLO DE SOFTWARE
TEMA: DERIVACION DE FUNCIONES ALGEBRAICAS
f ' (x)= lim∆x→0
5 (x+∆ x)+3−5 x−3∆x
f ' (x)= lim∆x→0
5 x+5∆ x+3−5 x−3∆ x
f ' (x)= lim∆x→ 0
5 ∆x∆ x
f ' (x)= lim∆x→0
¿5; f ' (x)=5
f ' (x)= lim∆x→0
¿¿
f ' (x)=lim∆ x→0
x2+2 x ∆x+∆x2+1−x2−1
∆ x
f ' (x)=lim∆ x→0
2 x ∆ x+∆ x2
∆ x
f ' (x)= lim∆x→0
¿)= lim∆ x→ 0
(2 x ∆ x∆ x
)+ lim∆ x→0¿)
f ' (x)= lim∆x→0
2x+ lim∆ x→0
∆ x
f ' (x)=2x
f ' (x)= lim∆x→0
5 x+5∆ x+104−5 x−104∆ x
f ' (x)= lim∆x→ 0
5 ∆x∆ x
f ' ( x )=5
f ' ( x )= lim∆ x→0
¿¿
f ' (x)=lim∆ x→0
x2+2 x ∆x+∆x2−1−x2+1
∆ x
f ' (x)=lim∆ x→0
2 x ∆ x+∆ x2
∆ x
f ' (x)= lim∆x→0
(2 x+∆ x )
f ' (x)=2x
f ' (x)= lim∆x→0
20 ( x+∆ x )+3 /4−20 x−3/4∆ x
f ' (x)= lim∆x→ 0
20 x+20∆ x+3/ 4−20x−3/4∆ x
f ' (x)= lim∆x→0
20 ∆ x∆ x
f ' (x)=20
f ' (x)= lim∆x→0
8¿¿
f ' (x)=lim∆ x→0
8x2+16 x ∆ x+8∆ x2+2−8 x2−2
∆ x
f ' (x)=lim∆ x→0
16 x ∆ x+8∆ x2
∆ x
f ' ( x )= lim∆ x→0
16 x+ lim∆ x→0
8 ∆ x
f ' ( x )=16 x
f ' (x)= lim∆x→0
35 ( x+∆ x )
−9− 35 x
+9
∆ x
f ' (x)= lim∆x→0
3 x5
+ 3∆ x5
−9−3 x5
+9
∆ x
f ' (x)= lim∆x→0
3 ∆ x5 ∆ x
f ' (x)=3/5
f ' (x)= lim∆x→0
5/2¿¿
f ' (x)=lim∆ x→0
52x2+5 x ∆x+∆ x2−100−5
2x2+100
∆ x
f ' (x)=lim∆ x→0
5 x ∆ x+∆ x2
∆ x
f ' ( x )= lim∆ x→0
(5 x+∆ x )
f ' ( x )=(5 x )
f ' (x)= lim∆x→0
910 ( x+∆ x )
+9− 910x
−9
∆ x
f ' (x)= lim∆x→0
9 x10
+ 9∆ x10
+9−9 x10
−9
∆ x
f ' (x)= lim∆x→0
9 x10
+ 9∆ x10
+9−9 x10
−9
∆ x
f ' (x)= lim∆x→0
9∆ x10 ∆x
f ' (x)=9/10
f' ( x )= lim
∆ x→0
3( x+∆ x )
−3x
∆x
f ' ( x )= lim∆ x→0
3x−3 ( x+∆x )x ( x+∆ x )∆ x
f ' ( x )= lim∆ x→0
−3∆ xx ( x+∆x )∆ x
f ' ( x )= lim∆ x→0
−3 ∆xx2∆x+x ∆ x2
¿¿
f ' (x)= lim∆x→ 0
[ x2∆ x+x ∆ x2
−3∆ x]−1
f ' (x)= lim∆x→ 0
[ x2+x ∆ x−3
]−1
f ' (x)= lim∆x→ 0
( −3x2+ x∆ x
)
f ' (x)=lim∆ x→0
−3
x2
f ' ( x )=−3 x−2
f ' (x)= lim∆x→0
53¿¿
¿¿
f ' (x)= lim∆x→ 0
5 x2−5¿¿¿¿
f ' (x)= lim∆x→0
5 x2−5 x2−10 x ∆x−5∆ x2
3x2 ¿¿¿
f ' (x)= lim∆x→ 0
5 x2−5 x2−10 x ∆x−5∆ x2
3x2 ¿¿¿
f ' (x)= lim∆x→0
−10 x ∆ x−5∆ x2
3 x2¿¿¿
f ' (x)= lim∆x→ 0
−10 x−5 ∆ x3 x2¿¿
¿
f ' ( x )=−10 x /3 x4=
f ' ( x )=−103 x3
f ' (x)= lim∆x→0
2¿¿
f ' (x)=lim∆ x→0
2 x3+6 x2∆ x+6 x ∆ x2+∆ x3+5−2 x3−5
∆ x
f ' (x)=lim∆ x→0
6x2∆ x+6 x ∆ x2+∆x3
∆x
f ' (x)= lim∆x→0
6 x2
f ' (x)=6 x2
f ' (x)= lim∆x→0
a(x+∆ x )+N−ax−N∆ x
f ' (x)= lim∆x→ 0
ax+a∆ x+N−ax−N∆x
f ' (x)= lim∆x→0
a∆ x∆ x
f ' (x)=a
f ' (x)= lim∆x→0
a¿¿
f ' (x)=lim∆ x→0
a x2+2a x ∆ x+a∆ x2+N−ax2−N
∆ x
f ' (x)=lim∆ x→0
2a x ∆ x+a∆ x2
∆ x
f ' ( x )= lim∆ x→0
( 2ax∆ x
+a∆ x )
f ' ( x )=2ax
f ' (x)= lim∆x→0
a¿¿
f ' (x)=lim∆ x→0
ax3+2ax2∆ x+2ax ∆ x2+a∆ x3+N−ax3−N
∆ x
f ' ( x )=lim∆ x→0
2ax2∆ x+2ax ∆ x2+a∆ x3
∆ x
f ' ( x )=2a x2
¿
f ' (x)= lim∆x→0
a¿¿
Donde (nk) son constantes
f ' (x)=lim∆ x→0
a xn+(n1)∆ x .a xn−1+(n2)∆x2 . a xn−2+…+( nn−1)ax∆ xn−1+(nn)a ∆ xn−a xn∆ x
f ' (x)=lim∆ x→0 (n1)∆ x .a xn−1+(n2)∆x2 . a xn−2+…+( nn−1)ax∆ xn−1+(nn)a∆ xn
∆ x
f ' (x)=lim∆ x→0 (n1)∆ x .a xn−1
∆ x+(n2)∆ x2 . a xn−2
∆ x+…+( nn−1)ax∆ xn−1
∆ x+(nn)a∆ xn
∆ x
f ' (x)= lim∆x→0
na xn−1+(n2)∆ x .axn−2+…+( nn−1)ax∆ xn−2+(nn)a ∆ xn−1
f ' ( x )=an xn−1
p) a
Si a es una constante entonces significa que no existe derivada.
Que: dxn /dx= nxn-1
Ejercicio 2. Calcula la derivada de las funciones.
Ejercicio 3. Calcula la derivada de las funciones.
u=x3 ; v=(x-1); u’=3x2; v’=1Sustituyendo nos da:
f(x)=(x+1); f’(x)=1; g1(x)=(x-3); g1’(x)=1
g’(x)=(x-3)+(x+3); g’(x)=2x-2
