Matematica

Determinar f’(x)
1. f(x)=2x-1 f’(x)=2
2. f(x)=x2+5 f’(x)=2x
3. f(x)=2x+1 =(2x+1)1/2
f'x=122x+112-1 2

f'x=12x+1

4. f(x)=1x+1=(x+1)-12

f'x=-12 x+1-32 1
f'x=-12(x+1)3

5.f(x)=x+1x-1 x-11-x+1(1)(x-1)2= -2(x-1)2

6. f(x)=3x2 -x +5 f’(x)=6x-1

7. f(x)=(2x+3)(3x-2)=6x2-4x+9x-6 f’(x)=12x+5

8. g(t)=(4t-7)2 g’(t)=2(4t-7)(4)= 32t-56

9. f(t)=1/(4-t2)= (4-t2)-1f’(t)=- (4-t2)-1-1 (2t)=-2t(4-t2)2

10. y=x+10x2

y’=x21-x+10(2x)(x2)2= x2-2x2+20xx4= -x2+20xx4= -x+20x3

11. y=x3 y’=3x2 P(2,8), m=3(2)2=12 Ec. Recta y-8=12(x-2)
12. y=3x2-4 y’=6xP(1,-1),m=6(1)=6 Ec. Recta y+1=6(x-1)
13. y=1/(x-1)=(x-1)-1 y’=-(x-1)-2 P(2,1),m=(2-1)-2 =1 Ec. Recta y-1=x-2

14. y=3x2-4x3 y’=-6x3--12x4 P(-1,7), m=6+12=18 Ec. Recta y-7=18(x+1)15. y=3x2x7+x+1 y’=x7+x+16x-3x2(7x6+1)(x7+x+1)2=6x7+6x2+6x-21x8-3x2(x7+x+1)2= 6x7+3x2+6x-21x8(x7+x+1)2

P(-1,3), m=-6+3-6-21(-1-1+1)2=-18 Ec. Recta y-3=-18(x+1)

16. Y=(x3)4 =x12y’=12x11 …………….(1)

u= x3 u’=3x2 ; y=u4 y’=4u3
dydx=dydu dudx = 4u3 (3x2)= 4(x3)3(3x2)=12x11 ………(2)
se cumple, son iguales (1) y (2)

17. y=(x2 - 1)2 = x4 – 2x2 + 1 y’=4x3-4x…………….(1)
u= x2 - 1 u’=2x y=u2 y’=2u
dydx=dydu dudx = 2u (2x) = 2(x2 - 1)(2x) = 4x3 -4x………(2) se cumple, son iguales (1) y (2)

18. Y=(1-x)3 = 1 – 3x + 3x2 -x3 y’ = -3 + 6x – 3x2…………….(1)
u=1-xu’=-1 y=u3 y’=3u2
dydx=dydu dudx = 3u2 (-1) = -3(1-x)2 = -3 + 6x – 3x2………(2) se cumple, son iguales (1)y(2)

19. Y=(x+1)4 = x4 + 4x3 +6x2 + 4x + 1 y’=4x3 + 12x2 + 12x + 4…………….(1)
u=x+1 u’=1 y=u4y’=4u3
dydx=dydu dudx = 4u3 (1) = 4(x+1) 3 = 4 (x3 + 3x2 + 3x + 1) ………(2) se cumple, son iguales (1)y(2)

1. f(x)=3 sen2x f’(x)=6senx cosx
2. f(x)=2cos4x f(x)=-8cos3x senx
3. f(x)=xcosxf’(x)=-xsenx+cosx
4. f(x)=√x senx f’(x)= -√x cosx – senx/(2√x)
5. f(x)=(senx)/x f’(x)=x cosx-senxx2
6. f(x)=sen2√x f’(x)=2senxcosx2x=senx cosxx
7. f(x)=(cos2x)/x...