Derivate fondamentali e regole di derivazione

Question 1

Derivata di f(x) = k

Answer 1

f’(x) = 0

Question 2

Derivata di f(x) = x^n

Answer 2

f’(x) = n x^n-1

Question 3

Derivata di f(x) = x

Answer 3

f’(x) = 1

Question 4

Derivata di f(x) = ^n√x

Answer 4

f’(x) = 1/n * ^n√x^n-1

Question 5

Derivata di f(x) = 1/x

Answer 5

f’(x) = - 1/x^2

Question 6

Derivata di f(x) = √x

Answer 6

f’(x) = 1/2 * √x

Question 7

Derivata di f(x) = sen(x)

Answer 7

f’(x) = cos(x)

Question 8

Derivata di f(x) = cos(x)

Answer 8

f’(x) = -sen(x)

Question 9

Derivata di f(x) = tg(x)

Answer 9

f’(x) = 1/cos^2(x) oppure 1+tg^2(x)

Question 10

Derivata di f(x) = ctg(x)

Answer 10

f’(x) = - 1/sen^2(x) oppure -(1+ctg^2(x)

Question 11

Derivata di f(x) = ln(x)

Answer 11

f’(x) = 1/x

Question 12

Derivata di f(x) = a^x

Answer 12

f’(x) = a^x * ln(a)

Question 13

Derivata di f(x) = e^x

Answer 13

f’(x) = e^x

Question 14

Derivata di f(x) = arcsen(x)

Answer 14

f’(x) = 1/√1-x^2

Question 15

Derivata di f(x) = arccos(x)

Answer 15

f’(x) = - 1/√1-x^2

Question 16

Derivata di f(x) = arctg(x)

Answer 16

f’(x) = 1/1+x^2

Question 17

f(x) = k*f(x)

Answer 17

f’(x) = k*f’(x)

Question 18

f(x) = f(x) + g(x)

Answer 18

f’(x) = f’(x) + g’(x)

Question 19

f(x) = f(x) * g(x)

Answer 19

f’(x) = f’(x)g(x) + f(x)g’(x)

Question 20

f(x) = f(x)/g(x)

Answer 20

f’(x) = ( f’(x)g(x) - f(x)g’(x) )/ g(x)^2

Question 21

f(x) = f(g(x))

Answer 21

f’(x) = f’(g(x)) * g’(x)

Question 22

f(x) = (f(x))^n

Answer 22

f’(x) = n(f(x))^n-1 * f’(x)

Question 23

f(x) = a^f(x)

Answer 23

f’(x) = a^f(x) * ln(a) * f’(x)

Question 24

f(x) = e^f(x)

Answer 24

f’(x) = e^f(x) * f’(x)