Ejercicio Calculo

fx=cos33x2sec24x3
fx=cos3x23sec4x32

f´x=sec4x32Dxcos3x23-cos3x23sec4x32sec4x322
f´x=sec4x323cos3x23-sec4x326x-cos3x232sec4x3sec 4x3tan4x312x2sec4x34
f´x =18x sec2 4x3 cos2 3x2 sen3x2-24x2 cos3 3x2sec2 4x3 tan4x3sec4 4x3
f´x = sec2 4x3(-18x cos2 3x2 sen 3x2-24x2 cos3 3x2 tan4x3)sec2 4x3 (sec2 4x3)

f´x = -18x cos2 3x2 sen 3x2-24x2 cos3 3x2 tan4x3 sec2 4x3

1.y=(Arc secx2)3

y´=3(Arc secx2)2DxArc secx2

y´=3(Arc secx2)22xx2x22-1

y´=3(Arc secx2)22xx22-1

y´=6(Arc secx2)2x2x4-1

2. gx=arccos 4-2x3

gx=-Dx 4-2x31-4-2x32gx=-6x21-4-2x32

3. y=log7arctanx3

y´=Dxarctanx3arctan x3 log7 e

y´=-Dxx31+x32 acttanx3log7 e

y´=-3x21+3x6 acttanx3log7 e

y´=-3x21+3x6arctan x3 log7 e

4. In arccot 2x3y´=Dx arccot 2x3arccot 2x3

y´=-Dx2x31+2x32arccot 2x3

y´=-6x21+4x6arccot 2x3
y´=-6x21+4x6arccot 2x3
y´=-6x21+4x6arccot 2x3

5. fx=tan24x-1+In (cot e5x+6)

f´x=tan24x-1cot24x-1Dx24x-1+Dxcot e5x+6cot e5x+6

f´x=tan24x-1cot 24x-124x-1 In 24+Dxtan2 (e5x+6)e5x+6cot e5x+6

f´x=4 tan24x-1cot 24x-124x-1 In 2+Dx4 tan2 (e5x+6)e5x+6cot e5x+6

6. Obtén la segundaderivada de:

y=cos2x3

y´=- sen 2x3(6x2)

y´=6x2- sen 2x3

y´´=6x2Dx- sen 2x3- sen 2x3 Dx 6x2

y´´=6x2- (cos 2x3)6x2- sen 2x3 12x

y´´=-36x4cos 2x3- 12x sen 2x3

7.Si fx=2x4-3x3+5x2-7x+9 , Obtén Dx4 f(x)

f´x=8x3-9x2+10x-7

f´´x=24x2-18x+10

fIIIx=48x-18

fIVx=48

8. Obtén y´ a partir de : secx3y2+17x6y7+12x4=13y5
Derivarrespecto a x:
secx3y2tanx3y2Dx x3y2+17x6Dx y7+ y7Dx 17x7+48x3=65y4y´
secx3y2tanx3y2x3 2y3 y´+y2 3 x2+17x6 7y6 y´+ y7+102x5 y7+48x3=65y4y´
2x3 y y´secx3y2tanx3y2+3 x2 y2secx3y2tanx3y2+119x6y6 y´+102x5y7+48x3=65y4y´

y´=2x3y secx3y2tanx3y2+119x6y6-65y4=-3 x2 y2secx3y2tanx3y2-102x5y7-48x3

y´=-3 x2 y2secx3y2tanx3y2-102x5y7-48x32x3y secx3y2tanx3y2+119x6y6-65y4

9.