Formules de dérivation

Question 1

(a^x)’

Answer 1

a^x * ln * a

Question 2

(e^x)’

Answer 2

e^x

Question 3

(log_a (x))’

Answer 3

1/(xlna)

Question 4

(ln (x))’

Answer 4

1/x

Question 5

(a^f(x))’

Answer 5

a^(f(x)) * lna * ln(x)

Question 6

(e^f(x))’

Answer 6

e^f(x) * f’(x)

Question 7

(log_a f(x))’

Answer 7

(1/(f(x) * ln a)) * f’(x)

Question 8

(ln f(x))’

Answer 8

(1/f(x)) * f’(x)

Question 9

(sinx)’

Answer 9

cosx

Question 10

(cosx)’

Answer 10

-sinx

Question 11

(tanx)’

Answer 11

sec^2(x)

Question 12

(cotx)’

Answer 12

-csc^2(x)

Question 13

(secx)’

Answer 13

secx * tanx

Question 14

(cscx)’

Answer 14

-cscx * cotx

Question 15

(sinf(x))’

Answer 15

cos(f(x)) * f’(x)

Question 16

(cosf(x))’

Answer 16

-sin(f(x)) * f’(x)

Question 17

(tanf(x))’

Answer 17

(sec^2 f(x)) * f’(x)

Question 18

(cotf(x))’

Answer 18

(-csc^2 f(x))* f’(x)

Question 19

(secf(x))’

Answer 19

(secf(x) * tanf(x)) * f’(x)

Question 20

(cscf(x))’

Answer 20

(-cscf(x) * cotf(x)) * f’(x)

Question 21

(arcsinx)’

Answer 21

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

Question 22

(arccosx)’

Answer 22

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

Question 23

(arctanx)’

Answer 23

1/(1+(x^2))

Question 24

(arccotx)’

Answer 24

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

Question 25

(arcsecx)’

Answer 25

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

Question 26

(arccscx)’

Answer 26

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

Question 27

(arcsinf(x))’

Answer 27

( 1/racine(1-(f(x)^2)) ) * f’(x)

Question 28

(arccosf(x))’

Answer 28

( -1/racine(1-(f(x)^2)) ) * f’(x)

Question 29

(arctanf(x))’

Answer 29

( 1/(1+(f(x)^2)) ) * f’(x)

Question 30

(arccotf(x))’

Answer 30

( -1/(1+(f(x)^2)) ) * f’(x)

Question 31

(arcsecf(x))’

Answer 31

( 1/|f’(x)|racine((f’(x))^2)-1) ) * f’(x)

Question 32

(arccscf(x))’

Answer 32

( -1/|f’(x)|racine((f’(x))^2)-1) ) * f’(x)