# Talleres

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TRABAJO DE CÁLCULO DIFERENCIAL
TALLER No 6

Enlos ejercicios 1 – 36 hallar la derivada de la función dada.

1. y = x2 – ½ x 2. y = 5 + sen x 3. y = [pic] - 3 sen x
4. g (t) = [pic] cost 5. f (x) = 4 [pic] + 3 cos x
6. f (x) = 2 sen x + 3 cos x 7. f (x) = t2 sen t 8. f(x) = [pic]
9. g (t) = [pic] 10. f(ө) = (ө + 1)cos ө 11. y = tg x – x
12. y = x + ctg x 13. y = 5x csc x 14. y = [pic] 15. f(ө)= - csc ө – sen ө
16. h(x) = x sen x + cos x 17. g(t)= t2 sen t +2t cos t – 2 sen t
18. h(ө) = 5 sec 3 ө + 3 ө 19. f(x)= sen [pic]x cos [pic]x 20. f (x) = tg 2x ctg 2x
21. y = [pic] 22. y = [pic]23. y = cos 3x 24. y = sen 2x
25. y = 3 tg 4x 26. y = 2 cos [pic] 27. y = sen [pic]x 28. y = sec x2
29. y = ¼ sen2x 30. y = 5cos2[pic]x 31. y = ¼ sen2 2x 32. y = 5 cos [pic]x)2
33. y = [pic] 34. y = csc24x 35.y = sec3 2x 36. y = x2sen [pic]

RESPUESTAS A LOSPROBLEMAS IMPARES
1. 2x + ½ sen x 3. -[pic] - 3 sen x 5. [pic] 7. t(tcos t + 2 sen t)
9. [pic] 11. -1 + sec2 x = tg2x 13. -5x csc xctg x + 5 csc x = 5 csc x(1 – x ctg x)
15. csc ө ctg ө – cos ө = ctg2 ө
17. t2cos t + 2t sen t – 2tsen t + 2 cos t – 2 cos = t2cos t
19. [pic] cos2[pic]x 21. [pic] 23. -3 sen 3x 25. 12 sec24x 27.[pic] cos [pic]x
29. ¼ sen 2x 31. ½ sen 4x 33. ½ ctg x[pic] 35. 6 sec3 2x tg 2x