Ejercicio 1
edit
y
=
(
3
x
5
−
1
)
(
2
x
+
3
)
{\displaystyle \ y=(3x^{5}-1)(2x+3)}
y
′
=
(
3
x
5
−
1
)
(
2
)
+
(
2
x
+
3
)
(
15
x
4
)
{\displaystyle \ y'=(3x^{5}-1)(2)+(2x+3)(15x^{4})}
y
′
=
6
x
5
−
2
+
30
x
5
+
45
x
4
{\displaystyle \ y'=6x^{5}-2+30x^{5}+45x^{4}}
y
′
=
36
x
5
+
45
x
4
−
2
{\displaystyle \ y'=36x^{5}+45x^{4}-2}
Ejercicio 2
edit
y
=
6
x
4
+
3
x
3
+
6
x
2
−
8
x
+
2
{\displaystyle \ y=6x^{4}+3x^{3}+6x^{2}-8x+2}
y
′
=
24
x
3
+
9
x
2
+
12
x
−
8
{\displaystyle \ y'=24x^{3}+9x^{2}+12x-8}
Ejercicio 3
edit
f
(
x
)
=
c
o
s
(
x
)
{\displaystyle \ f(x)=cos(x)}
f
′
(
x
)
=
l
i
m
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
{\displaystyle f'(x)=lim_{h\to 0}{\frac {f(x+h)-f(x)}{h}}}
f
′
(
x
)
=
l
i
m
h
→
0
c
o
s
(
x
+
h
)
−
c
o
s
x
h
{\displaystyle f'(x)=lim_{h\to 0}{\frac {cos(x+h)-cosx}{h}}}
lim
h
→
0
c
o
s
(
x
)
∗
c
o
s
(
h
)
−
s
e
n
(
x
)
∗
s
e
n
(
h
)
−
c
o
s
(
x
)
h
{\displaystyle \lim _{h\to 0}{\frac {cos(x)*cos(h)-sen(x)*sen(h)-cos(x)}{h}}}
lim
h
→
0
c
o
s
(
x
)
(
c
o
s
h
−
1
)
h
∗
s
e
n
(
x
)
s
e
n
(
h
)
h
{\displaystyle \lim _{h\to 0}{\frac {cos(x)(cosh-1)}{h}}*{\frac {sen(x)sen(h)}{h}}}
cos
(
x
)
∗
l
i
m
h
→
0
c
o
s
(
h
)
−
1
h
−
s
e
n
(
l
i
m
h
→
0
s
e
n
(
h
)
h
{\displaystyle \cos(x)*lim_{h\to 0}{\frac {cos(h)-1}{h}}-sen(lim_{h\to 0}{\frac {sen(h)}{h}}}
lim
h
→
0
0
∗
c
o
s
(
x
)
−
l
i
m
h
→
0
1
∗
−
s
e
n
(
x
)
{\displaystyle \lim _{h\to 0}\ 0*cos(x)-lim_{h\to 0}\ 1*-sen(x)}
0
−
s
e
n
(
x
)
{\displaystyle \ 0-sen(x)}
−
s
e
n
(
x
)
{\displaystyle \ -sen(x)}
Ejercicio 4
edit
f
(
x
)
=
x
∗
e
−
x
{\displaystyle \ f(x)=x*e^{-x}}
f
′
(
x
)
=
e
−
x
(
1
−
x
)
{\displaystyle \ f'(x)=e^{-x}(1-x)}
Ejercicio 5
edit
f
(
x
)
=
5
x
5
+
4
x
4
+
3
x
3
+
2
x
2
+
x
{\displaystyle \ f(x)=5x^{5}+4x^{4}+3x^{3}+2x^{2}+x}
f
′
(
x
)
=
25
x
4
+
16
x
3
+
9
x
2
+
4
x
+
1
{\displaystyle \ f'(x)=25x^{4}+16x^{3}+9x^{2}+4x+1}
![{\displaystyle \lim _{t\ 0}{\frac {(}{\sqrt[{2}]{2t}}})-{\sqrt[{2}]{2}}){t}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/852c17b46d152b7496238f7866a5c6f3138bb01b)
![{\displaystyle \lim _{t\ 0}{\frac {{\sqrt[{2}]{2t}}-{\sqrt[{2}]{2}}}{t}}*{\sqrt[{2}]{2t}}+{\sqrt[{2}]{2}}{\sqrt[{2}]{2t}}+{\sqrt[{2}]{\sqrt[{2}]{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d65b1fe8593dbf2e2229e8cd3b9cd6ae25c6cf2e)
![{\displaystyle \lim _{t\ 0}{\frac {-t}{t({\sqrt[{2}]{2t}}+{\sqrt[{2}]{)}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/da61cd41a22b68a85128db2dc1409c4260aac8c3)
![{\displaystyle \lim _{t\ 0}{\frac {-1}{({\sqrt[{2}]{2t}}+{\sqrt[{2}]{)}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0c1341591495ae01ebdb1e2e6f964063b44e6d36)
![{\displaystyle {\frac {-1}{({\sqrt[{2}]{2*0}}+{\sqrt[{2}]{)}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/05b503cb2831d0166108f687ae66c5f4da88c652)
![{\displaystyle {\frac {-1}{({0}+{\sqrt[{2}]{2}})}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/27ac05d9f4d49cad4bfc97094e08fdea6b96f4ba)
![{\displaystyle {\frac {-1}{({\sqrt[{2}]{2}})}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d676eccc871f5a12e06d149def24b65fe4dced9)
