Ejercicios matemáticas

1. y=
rpta:
√(1-x)m(1+x)n
m+n
(n-m)-(n+m)x
(n+m)n+m√(1-x)n(1+x)m
2.
Rpta :
y= √x+√x+√x
1+2√x+4√x√x+√x
(x>0)
8√x√𝑥√x√x√x√𝑥
3. Y= sen(cos2x).cos(sen2x)
Rpta: -sen 2x.cos(cos2x)
4. Y=
senx-xcosx
Cosx+xsenx
x2
Rpta:
(cosx+xsenx)2
tgx-1 tg3x+ 1 tg5x
3
5
6
Rpta: 1+tg x
5. Y=
6. Y= 1-x2 sin x-(1+x)2cosx
2
2
Rpta: x2e-xsenx
7. Y=
1
+ 1
4)
4(1+x
4
Rpta:
8. Y =
Rpta
ln
1
X(1+x4)2
1
2√6
1
2
3x -2
x4
1+x4
(x=0)
ln x√3-√2
x√3+√2
9. Y= xln2(x√1+x2)-2√1+x2 ln(x+√1+x2)+2x
Rpta: ln2(x+√x2+1)
10. Y= ln b+acosx+√b2-a2sinx
a+bcosx
rpta:
√ b2-a2
a+bcosx
11. Y= 1 (ln3 x+3ln2 x+6+ln x+6)
X
Rpta. ln3 x
(x>0)
2
X
12. Y= ln
Rpta :
1 + ln 1 + ln 1
X
x
x
1+x+ 1+ ln 1
X
x
1+xln 1
X
1+xln 1 +ln 1
x
x
13. Y= ln tg x – cosx.ln tgx
2
Rpta. sen xln tgx
14. Y= x arcosen √ x + arctg √x-√x
1+x
Rpta. arcosin
15. Y= aecotg sen x+ cos x
Sen x- cos x
Rpta. (x =π +kπ, es entero
4
16. Y= arcosen 1-x2
rpta. -2sgn x
2
1+ x
1+x2
17. Y= 1 ln (x+1)2 + 1 arctg 2x-1
6
x2-x+1
√3
√3
Rpta.
1
X3 +1