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Cálculo Antiderivadas y Derivadas
  • 1. Hallar la derivada de (x+2)/(x+1)
A) 1/(x + 1)2
B) - 1/(x - 1)2
C) - 1/(x + 1)
D) - 1/(x + 1)2
  • 2. Hallar la derivada de 1/(x4+x2+1)
A) - 2·x·(2·x2 + 1)/(x4 + x2 + 1)
B) x·(2·x2 + 1)/(x4 + x2 + 1)2
C) - 2·x·(2·x2 + 1)/(x4 + x2 + 1)2
D) - 2·x·(2·x+ 1)/(x4 + x2 + 1)2
  • 3. Hallar la derivada de ex/(x+ex)
A) ex·(x - 1)/(ex + x)2
B) -ex·(x - 1)/(ex + x)2
C) ex·(x + 1)/(ex - x)2
D) ex·(x - 1)/(ex + x)
  • 4. Hallar la derivada de ex·(1+3x2+5x4)
A) -ex·((5·x4 + 3·x2 + 1) - 20·x3 - 6·x)
B) ex·((5·x4 + 3·x2 + 1) + 20·x3 + 6)
C) ex·((5·x4 + 3·x2 + 1)·LN(e) + 20·x2 + 6·x)
D) ex·((5·x4 + 3·x2 + 1) + 20·x3 + 6·x)
  • 5. Hallar la derivada de senx/(1+cosx)
A) -1/(COS(x) - 1)
B) 1/(COS(x) + 1)
C) -1/(SEN(x) + 1)
D) 1/(SEN(x) + 1)
  • 6. Hallar la derivada de tanx/x
A) SEC(x)2/X - TAN(x)/x2
B) SEC(x)2/X + TAN(x)/x2
C) SEC(x)2/X - TAN(x)/x
D) -SEC(x)2/X - TAN(x)/x2
  • 7. Hallar la derivada de x/(senx+cosx)
A) ((x + 1)·SIN(x) - (x - 1)·COS(x))/(COS(x) + SIN(x))2
B) ((x + 1)·SIN(x) - (x - 1)·COS(x))/(COS(x) - SIN(x))2
C) ((x + 1)·SIN(x) - (x - 1)·COS(x))/(COS(x) + SIN(x))
D) -((x - 1)·SIN(x) + (x - 1)·COS(x))/(COS(x) + SIN(x))2
  • 8. Hallar la derivada de x3cosx
A) 3·x2·COS(x) - x3·SIN(x)
B) 3·x2·COS(x) + x2·SIN(x)
C) -3·x2·COS(x) - x3·SIN(x)
D) 3·x2·COS(x) - x3·COS(x)
  • 9. Hallar la derivada de ex.tanx
A) -ex·(TAN(x) + SEC(x)2)
B) ex·(TAN(x) + CSC(x)2)
C) e2X·(TAN(x) - SEC(x)2)
D) ex·(TAN(x) + SEC(x)2)
  • 10. Calcular ∫(4·SIN(x) - 3·x5 + 6·x3/4)dx
A) - 4·COS(x) - x5/2 + 24·x7/4/7 + c
B) 4·COS(x) - x6/2 + 24·x7/4/7 + c
C) - 4·COS(x) - x6/2 + 24·x7/4 + c
D) - 4·COS(x) - x6/2 + 24·x7/4/7 + c
  • 11. Calcular ∫(ex+20/(1+x2))dx
A) -20·ATAN(x) - ex + c
B) 20·TAN(x) + ex + c
C) -20·TAN(x) + ex + c
D) 20·ATAN(x) + ex + c
  • 12. Calcular ∫(4/√(1-x2))dx
A) 4·ASIN(x) + c
B) -4·ASIN(x) + c
C) 4·ACOS(x) + c
D) -4·SIN(x) + c
  • 13. Calcular ∫(3√x-1/√x)dx
A) 2·x3/2 - 2·√x + c
B) 2·x1/2 - 2 + c
C) -x3/2 - 2
D) 2·x3/2 + 2+c
  • 14. Calcular ∫(x2+3cosx)dx
A) 3·COS(x) - x3/3 + c
B) 3·SIN(x) - x3/2 + c
C) 3·SIN(x) + x3/3 + c
D) -SIN(x) + x3/3 + c
  • 15. Calcular ∫(3·ex + 5·SEC(x)2)dx
A) 3·ex - 3 - TAN(x) + c
B) -ex + 5·TAN(x) + c
C) -3·ex - 3 + 5·COT(x) + c
D) 3·ex + 5·TAN(x) + c
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