Derivadas

Tarea IV
L. F. Andrés Hernández Pascual*
1.-
3x4dx=3x4dx=3x45+c= x55+c
2.-
2x7dx=2x7dx=2x88+c= 2x88+c
3.-
1x3 dx=1x-3dx=1x-2-2+c= -12x2+c
4.-
3t3 dt=3t-5dt=3t-4-4+c= -34t4+c
5.-5u3/2du=5u3/2du=5u5/252+c= 10u5/25+C=2u5/2 +c
6.-
3x dx= 5x-1/3 dx=2x2/323+c= 3x2/3+C=33x2 +c
7.-
3u5-2u3du=3u5du-2u3du=3u36-2u44=u62-u42+c
8.-
y32y3-3dy=2y5-3y3dy=2y5dy-3y3dy= 2y66-3y44+c9.
x45-x2dx=5x4-x6dx=5x4dx-1x6dx=5x55-x77=x5-x77+c

10.-
8x4+4x3-6x2-4x+5dx=8x4dx+4x3dx-6x2dx-4xdx+5dx=
8x55+4x44-6x33-4x22+5x1=8x55+x4-2x3-2x2+5x+c
11.-
2+3x2-8x3dx=2dx+3x2dx-8x3dx=2x+3x33-8x44=2x+x3-2x4+c
12.-
x x+1dx=x2/3+x1/2=1x3/2 dx+1x1/2 dx=
1x5/252+1x2/323=2x5/25+2x2/33+c
13.-
x -1x dx=x1/2-x-1/2=1x1/2 dx-1x-1/2 dx=
1x3/232-1x1/212=2x3/23+2x1/2+c

14.- 2x3 + 3x2+5dx = (2x-3+ 3x-2 +5)dx = 2x-3dx + 3x-2dx + 5dx = 2x-2-2+ 3x-1-1+ 5x = -x-2-3x-1 +5x +c =
-1x2-3x +5x +c

15.- 3-1x4+1x2dx = 3-x-4+x-2dx = 3dx - 1x-4dx+1x-2dx = 3x - 1x-3-3 + 1x-1-1 = 3x + x-33 - x-1 + c = 3x + 13x3 - 1x + c

16.- x2+4x-4xdx = (x2 + 4x - 4)x-12 = x32 + 4x12-4x-12 =1x32 dx + 4x12 dx- 4x-12 dx = 1x5252 + 4x3232 - 4x1212 =
2x525+8x323-8x12+c

17.- y4-2y2-1ydy= y4+2y2-1(y)-12dy = y72 + 2y32 - y-12dy = 1y72 dy + 2y32 dy - 1y-12 dy= 1y9292 +2y5252 - 1y1212 = 2y929 + 4y525 - 2y12 + c

18.-3x+1xdx=x13+x-12dx=1x13dx+1x-12dx=13x434+12x12
=3x434+2x12+c

19.27t3-13tdt =27t3-1 t-13dt = 27t83 - t-13 dt= 27t83dt-1t-13dt =27t113113 - 1t2323 = 81t11311 - 3t232 + c

20.-3sin t-2cos tdt= 3sint dt - 2cost dt = -3cost-2sint +c

21.- 5 cosx-4 senxdx=5 cosx dx-4 senx dx =5senx+4cosx+c

22.-senxcos2xdx=(-du)u2=-duu2=-u-2du
Solución =-u-1-1+c=u-1+c
u=cosx =1u+c
du=-senxdx...