13 calculo de derivadas(1)

Cálculo de derivadas (1) __________________ Aplica las fórmulas elementales de derivación para calcular las derivadas de las funciones siguientes:

1) f (x) = 4x3 − 2x2 + 3x −10 2) f (x) = 2 ⋅senx − 3 ⋅ cos x + 4

3) f (x) = 3 ⋅ tanx − 4 ⋅sec x 4) f (x) = 2 ⋅ cotanx + 3 ⋅ cosec x

5) f (x) = 2

x3 6)

f (x) = 4

x3− 3

x2+ 2

x+1

7) f (x) = 2 ⋅ x + 5 8) f (x) = x23 − 4 ⋅ x3 + 5

9)

f (x) = 3

x43+ 3

x23+10 10)

f (x) = 1

3x2+ 2 ⋅ x − 1

2 ⋅ x3

11) f (x) = 2 ⋅ex + 3 12) f (x) = 1

2⋅ lnx + 3

13) f (x) = 1 + lnx2 14) f (x) = x + ln x

2

15) f (x) = (x + 2) ⋅(x − 4) 16) f (x) = (x2 + 2) ⋅(x2 +1)

17) f (x) = (x3 −1) ⋅(x3 +1) 18) f (x) = x + 4( ) ⋅ x3 − 5( )

19) f (x) = x2 ⋅ cos x 20) f (x) = x2 ⋅ tanx − 2x + 5

21) f (x) = (2x + senx) ⋅(x2 + 4) 22) f (x) = x4 ⋅(2senx − 3cos x)

23) f (x) = (x + senx) ⋅(4 + cos x) 24) f (x) = (sec x + tanx) ⋅(senx + cos x)

25) f (x) = x2 ⋅ex 26) f (x) = ex ⋅ lnx

27) f (x) = ex ⋅ cos x 28) f (x) = (1 − lnx) ⋅(2 + 3 ⋅ lnx)

29) f (x) = x2 +1

x2 + 5 30)

f (x) = 2x − 3

x2 − 3x + 2

31) f (x) = 2x2 + x −1

3x + 2 32)

f (x) = x

x +1

33)

f (x) = 2x +1

1 − x 34)

f (x) = x +1

3 x3 + 2

35) f (x) = 1 + senx

1 − senx 36)

f (x) = senx + cos x

senx − cos x

37) f (x) = 1 + tanx

1 − tanx 38)

f (x) = x2 senx

1 + x2

39) f (x) = 2 + 3 ⋅ lnx

1 − 4 ⋅ lnx 40)

f (x) = x2 ⋅ex

1 + ex