Reglas de Derivación: Aprende a Calcular Derivadas Fácilmente

Question 1

Determina la derivada de la función f(x) = e^(3x).

Accepted Answer

f'(x) = 3e^(3x)

Answer

f'(x) = x e^(3x)

Answer

f'(x) = 1 / (3x)

Answer

f'(x) = e³

Question 2

Determina la derivada de la función f(x) = |x|.

Accepted Answer

f'(x) = 1 si x > 0, f'(x) = -1 si x < 0

Answer

f'(x) = 0

Answer

f'(x) = -1

Answer

f'(x) = 1

Question 3

Calcula la derivada de la función g(x) = (x³ + 1)^(1/2).

Accepted Answer

g'(x) = (3x²) / (2(x³ + 1)^(1/2))

Answer

g'(x) = (2x) / (x³ + 1)^(1/2)

Answer

g'(x) = (3x²) / (x³ + 1)

Answer

g'(x) = (x³ + 1)^(1/2)

Question 4

Determina la derivada de la función f(x) = arctan(x).

Accepted Answer

f'(x) = 1 / (1 + x²)

Answer

f'(x) = arctan(1 / x)

Answer

f'(x) = 1

Answer

f'(x) = -1 / (1 + x²)

Question 5

Calcula la derivada de la función g(x) = (sen(x) + cos(x)) / (sen(x) - cos(x)).

Accepted Answer

g'(x) = (2 cos²(x) - 2 sen²(x)) / (sen(x) - cos(x))²

Answer

g'(x) = (cos(x) - sen(x)) / (sen(x) + cos(x))

Answer

g'(x) = (cos(x) + sen(x)) / (sen(x) - cos(x))

Question 6

Determina la derivada de la función f(x) = x^x.

Accepted Answer

f'(x) = x^x (1 + ln(x))

Answer

f'(x) = x^x

Answer

f'(x) = x^x ln(x)

Answer

f'(x) = ln(x) / x

Question 7

Halla la derivada de f(x) = x^2 * e^x usando la regla del producto:

Accepted Answer

2xe^x + x^2 * e^x

Answer

xe^x - x^2 * e^x

Answer

xe^x + x^2 * e^x

Answer

2xe^x - x^2 * e^x

Question 8

Encuentra la derivada de la función f(x) = 3x² - 2x + 1.

Accepted Answer

f'(x) = 6x - 2

Answer

f'(x) = 3x - 2

Answer

f'(x) = 9x - 2

Answer

f'(x) = 6x + 1

Question 9

¿Cuál es la derivada de la función f(x) = e^x?

Accepted Answer

f'(x) = e^x

Answer

f'(x) = x*e^x

Answer

f'(x) = e^(2x)

Answer

f'(x) = 1

Question 10

Calcula la derivada de la función f(x) = ln(x).

Accepted Answer

f'(x) = 1/x

Answer

f'(x) = x

Answer

f'(x) = ln(x²)

Answer

f'(x) = 1/(x²)

Question 11

Determina la derivada de la función f(x) = sen(x).

Accepted Answer

f'(x) = cos(x)

Answer

f'(x) = tan(x)

Answer

f'(x) = x*cos(x)

Answer

f'(x) = -sen(x)

Question 12

Encuentra la derivada de la función f(x) = (x² + 3x - 2)⁴.

Accepted Answer

f'(x) = 4(x² + 3x - 2)³(2x + 3)

Answer

f'(x) = 4x(x² + 3x - 2)³

Answer

f'(x) = (x² + 3x - 2)³

Answer

f'(x) = 4(x² + 3x - 2)⁴(2x + 3)

Question 13

Encuentra la derivada de la función f(x) = e^(x² + 1).

Accepted Answer

f'(x) = 2xe^(x² + 1)

Answer

f'(x) = e^(x² + 1)

Answer

f'(x) = x*e^(x² + 1)

Answer

f'(x) = 2x²*e^(x² + 1)

Question 14

Calcula la derivada de la función f(x) = ln(x² + y²), donde y es una constante.

Accepted Answer

f'(x) = 2x/(x² + y²)

Answer

f'(x) = x/(x² + y²)

Answer

f'(x) = 2y/(x² + y²)

Answer

f'(x) = 1/(x² + y²)

Question 15

Calcula la derivada de la función f(x) = 3x² + 2x - 1.

Accepted Answer

f'(x) = 6x + 2

Answer

f'(x) = 3x

Answer

f'(x) = 12x - 1

Answer

f'(x) = 9x + 2

Question 16

Calcula la derivada de la función h(x) = 4√x.

Accepted Answer

h'(x) = 2/√x

Answer

h'(x) = 4/√x

Answer

h'(x) = 2√x

Answer

h'(x) = 4x

Question 17

Encuentra la derivada de la función y = 2/x³.

Accepted Answer

y' = -6/x⁴

Answer

y' = -6/x³

Answer

y' = 6/x⁴

Answer

y' = 2/x⁴

Question 18

Encuentra la derivada de la función q(x) = e^x + ln(x).

Accepted Answer

q'(x) = e^x + 1/x

Answer

q'(x) = e^x - 1/x

Answer

q'(x) = ln(x)

Answer

q'(x) = e^x

Question 19

Calcula la derivada de la función t(x) = sin(x²).

Accepted Answer

t'(x) = 2xcos(x²)

Answer

t'(x) = cos(x²)

Answer

t'(x) = 2xsin(x²)

Answer

t'(x) = -2xcos(x²)

Question 20

La derivada de la función f(x) = 3x^2 + 2x - 1 es:

Accepted Answer

6x + 2

Answer

3x + 2

Answer

6x^2 + 2x

Answer

9x + 2

Question 21

Si f(x) = sin(x), entonces f'(x) es:

Accepted Answer

cos(x)

Answer

tan(x)

Answer

sec(x)

Answer

-sin(x)

Question 22

La derivada de la función f(x) = e^x es:

Accepted Answer

e^x

Answer

ln(x)

Answer

x * e^(x-1)

Answer

1/x

Question 23

La derivada de la función f(x) = ln(x) es:

Accepted Answer

1/x

Answer

e^x

Answer

ln(1/x)

Answer

x

Question 24

Si f(x) = x^3 + 2x^2 - 5x, ¿cuál es el valor de f'(2)?

Accepted Answer

17

Answer

12

Answer

21

Answer

10

Question 25

La regla de la cadena establece que la derivada de f(g(x)) es:

Accepted Answer

f'(g(x)) * g'(x)

Answer

f'(g(x)) + g'(x)

Answer

f'(x) * g'(x)

Answer

f(g'(x)) * g(x)

Question 26

La derivada de la función f(x) = (x^2 + 1)^3 es:

Accepted Answer

6x(x^2 + 1)^2

Answer

3(x^2 + 1)^2

Answer

3x^2(x^2 + 1)^2

Answer

6x^2(x^2 + 1)^2

Question 27

La derivada de la función f(x) = x * sin(x) es:

Accepted Answer

sin(x) + x * cos(x)

Answer

x * cos(x)

Answer

sin(x) - x * cos(x)

Answer

cos(x)

Question 28

La derivada de la función f(x) = (x^2 + 1)/(x - 1) es:

Accepted Answer

(x^2 - 2x - 1)/(x - 1)^2

Answer

(2x)/(x - 1)

Answer

(x^2 + 1)/(x - 1)^2

Answer

(x^2 + 2x + 1)/(x - 1)^2

Question 29

La derivada de la función f(x) = 2^x es:

Accepted Answer

2^x * ln(2)

Answer

ln(2)

Answer

2^x

Answer

x * 2^(x-1)

Question 30

Dada la función f(x) = 3x² + 2x - 1, ¿cuál es su derivada?

Accepted Answer

f'(x) = 6x + 2

Answer

f'(x) = 3x + 2

Answer

f'(x) = 6x² + 2

Answer

f'(x) = 9x + 2

Question 31

¿Cuál es la derivada de la función f(x) = 5x³?

Accepted Answer

f'(x) = 15x²

Answer

f'(x) = 10x²

Answer

f'(x) = 5x²

Answer

f'(x) = 15x³

Question 32

Si g(x) = 4x⁻², ¿cuál es g'(x)?

Accepted Answer

g'(x) = -8x⁻³

Answer

g'(x) = -4x⁻³

Answer

g'(x) = 8x⁻³

Answer

g'(x) = -8x⁻²

Question 33

La derivada de la función f(x) = sin(x) es:

Accepted Answer

f'(x) = cos(x)

Answer

f'(x) = -cos(x)

Answer

f'(x) = -sin(x)

Answer

f'(x) = sin(x)

Question 34

Si h(x) = e^x, ¿cuál es h'(x)?

Accepted Answer

h'(x) = e^x

Answer

h'(x) = e^(x+1)

Answer

h'(x) = x*e^(x-1)

Answer

h'(x) = 1/e^x

Question 35

Calcula la derivada de la función f(x) = (2x + 1)(x - 3)

Accepted Answer

f'(x) = 4x - 5

Answer

f'(x) = 4x + 5

Answer

f'(x) = 2x - 5

Answer

f'(x) = 2x + 5

Question 36

Dada la función f(x) = (x² + 1)/(x - 2), ¿cuál es f'(x)?

Accepted Answer

f'(x) = (x² - 4x - 1)/(x - 2)²

Answer

f'(x) = (x² + 4x - 1)/(x - 2)²

Answer

f'(x) = (2x + 1)/(x - 2)²

Answer

f'(x) = (2x - 1)/(x - 2)²

Question 37

Si f(x) = ln(x), ¿cuál es f'(x)?

Accepted Answer

f'(x) = 1/x

Answer

f'(x) = ln(x)

Answer

f'(x) = 1/ln(x)

Answer

f'(x) = x

Question 38

Calcula la derivada de la función f(x) = cos(2x).

Accepted Answer

f'(x) = -2sin(2x)

Answer

f'(x) = 2sin(2x)

Answer

f'(x) = -sin(2x)

Answer

f'(x) = sin(2x)

Question 39

Encuentra la derivada de la función f(x) = (x³ + 2x)².

Accepted Answer

f'(x) = 2(x³ + 2x)(3x² + 2)

Answer

f'(x) = (x³ + 2x)(3x² + 2)

Answer

f'(x) = (x³ + 2x)(3x² - 2)

Answer

f'(x) = 2(x³ + 2x)(3x² - 2)