Formules

Question 1

Dérive (k)’

Answer 1

0

Question 2

Dérive (x)’

Answer 2

1

Question 3

Dérive (x^n)’

Answer 3

n*x^n-1

Question 4

Dérive (a^f(x))’

Answer 4

a^f(x) *ln(a) *f’(x)

Question 5

Dérive (loga f(x))’

Answer 5

( 1/(f(x)*ln(a) ) * f’(x)

Question 6

Dérive (sin f(x))’

Answer 6

cos f(x) * f’(x)

Question 7

Dérive (cos f(x))’

Answer 7

-sin f(x) * f’(x)

Question 8

Dérive (tan f(x))’

Answer 8

sec^2 f(x) * f’(x)

Question 9

Dérive (cot f(x))’

Answer 9

-csc^2 f(x) * f’(x)

Question 10

Dérive (sec f(x))’

Answer 10

sec f(x) *tan f(x) * f’(x)

Question 11

Dérive (csc f(x))’

Answer 11

-csc f(x) * cot f(x) * f’(x)

Question 12

Dérive (arcsin f(x))’

Answer 12

( 1/√(1-(f(x))^2 ) * f’(x)

Question 13

Dérive (arccos f(x))’

Answer 13

( -1/√(1-(f(x))^2) ) * f’(x)

Question 14

Dérive (arctan f(x))’

Answer 14

( 1/(1+(f(x))^2) ) * f’(x)

Question 15

Dérive (arccot f(x))’

Answer 15

( -1/(1+(f(x))^2) ) * f’(x)

Question 16

Dérive (arcsec f(x))’

Answer 16

( 1/(|f(x)|*√(f(x)^2-1)) ) * f’(x)

Question 17

Dérive (arccsc f(x))’

Answer 17

( -1/(|f(x)|*√(f(x)^2-1)) ) * f’(x)

Question 18

csc x = ?

Answer 18

1/sin x

Question 19

sec x = ?

Answer 19

1/cos x

Question 20

cot x = ?

Answer 20

1/tan x ou cos x/sin x

Question 21

tan x = ?

Answer 21

sin x/cos x

Question 22

intègre ∫x^r dx

Answer 22

(x^r+1)/(r+1) +c

Question 23

intègre ∫1/x dx

Answer 23

ln(x) +c

Question 24

intègre ∫cos x dx

Answer 24

sin x +c

Question 25

intègre ∫sin x dx

Answer 25

-cos x +c

Question 26

intègre ∫sec^2 x dx

Answer 26

tan x +c

Question 27

intègre ∫csc^2 x dx

Answer 27

-cot x +c

Question 28

intègre ∫sec x * tan x dx

Answer 28

sec x +c

Question 29

intègre ∫csc x * cot x dx

Answer 29

-csc x +c

Question 30

intègre ∫e^x dx

Answer 30

e^x +c

Question 31

intègre ∫a^x dx

Answer 31

(a^x)/((ln(a)) +c

Question 32

intègre ∫1/(√(1-x^2) dx

Answer 32

arcsin x +c

Question 33

intègre ∫1/(1+x^2) dx

Answer 33

arctan x +c

Question 34

intègre ∫1/(x√(x^2-1)) dx

Answer 34

arcsec x +c

Question 35

intègre ∫tan x dx

Answer 35

ln |sec x| +c ou -ln |cos x| +c

Question 36

intègre ∫cot x dx

Answer 36

ln |sin x| +c

Question 37

intègre ∫sec x dx

Answer 37

ln |sec x +tan x| +c

Question 38

intègre ∫csc x dx

Answer 38

-ln |csc x + cot x| +c ou
ln |csc x - cot x| +c ou
ln |cot x - csc x| +c

Question 39

Équation pour calculer une « partition »

Answer 39

Δx = (b-a)/n

Question 40

Équation pour trouver xi

Answer 40

xi = a + iΔx

Question 41

Identité trigo 1 (celle avec sin et cos)

Answer 41

sin^2(A) + cos^2(A) = 1

Question 42

Identité trigo 2 (celle avec sec et tan)

Answer 42

sec^2(A) = 1 + tan^2(A)

Question 43

Identité trigo 3 (celle avec csc et cot)

Answer 43

csc^2(A) = 1 + cot^2(A)

Question 44

Construction triangle sin

Answer 44

sinθ = O/H

Question 45

Construction triangle cos

Answer 45

cosθ = A/H

Question 46

Construction triangle tan

Answer 46

tanθ = O/A

Question 47

Construction triangle csc

Answer 47

cscθ = H/O

Question 48

Construction triangle sec

Answer 48

secθ = H/A

Question 49

Construction triangle cot

Answer 49

cotθ = A/O