Formules Flashcards by Élysabeth Boulet

Q

Dérive (k)’

A

0

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Q

Dérive (x)’

A

1

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Q

Dérive (x^n)’

A

n*x^n-1

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Q

Dérive (a^f(x))’

A

a^f(x) *ln(a) *f’(x)

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Q

Dérive (loga f(x))’

A

( 1/(f(x)*ln(a) ) * f’(x)

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Q

Dérive (sin f(x))’

A

cos f(x) * f’(x)

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Q

Dérive (cos f(x))’

A

-sin f(x) * f’(x)

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Q

Dérive (tan f(x))’

A

sec^2 f(x) * f’(x)

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Q

Dérive (cot f(x))’

A

-csc^2 f(x) * f’(x)

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Q

Dérive (sec f(x))’

A

sec f(x) *tan f(x) * f’(x)

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Q

Dérive (csc f(x))’

A

-csc f(x) * cot f(x) * f’(x)

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Q

Dérive (arcsin f(x))’

A

( 1/√(1-(f(x))^2 ) * f’(x)

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Q

Dérive (arccos f(x))’

A

( -1/√(1-(f(x))^2) ) * f’(x)

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Q

Dérive (arctan f(x))’

A

( 1/(1+(f(x))^2) ) * f’(x)

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Q

Dérive (arccot f(x))’

A

( -1/(1+(f(x))^2) ) * f’(x)

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Q

Dérive (arcsec f(x))’

A

( 1/(|f(x)|*√(f(x)^2-1)) ) * f’(x)

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Q

Dérive (arccsc f(x))’

A

( -1/(|f(x)|*√(f(x)^2-1)) ) * f’(x)

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Q

csc x = ?

A

1/sin x

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Q

sec x = ?

A

1/cos x

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Q

cot x = ?

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A

1/tan x ou cos x/sin x

Q

tan x = ?

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A

sin x/cos x

Q

intègre ∫x^r dx

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A

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

Q

intègre ∫1/x dx

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A

ln(x) +c

Q

intègre ∫cos x dx

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A

sin x +c

intègre ∫sin x dx

-cos x +c

intègre ∫sec^2 x dx

tan x +c

intègre ∫csc^2 x dx

-cot x +c

intègre ∫sec x * tan x dx

sec x +c

intègre ∫csc x * cot x dx

-csc x +c

intègre ∫e^x dx

e^x +c

intègre ∫a^x dx

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

intègre ∫1/(√(1-x^2) dx

arcsin x +c

intègre ∫1/(1+x^2) dx

arctan x +c

intègre ∫1/(x√(x^2-1)) dx

arcsec x +c

intègre ∫tan x dx

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

intègre ∫cot x dx

ln |sin x| +c

intègre ∫sec x dx

ln |sec x +tan x| +c

intègre ∫csc x dx

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

Équation pour calculer une « partition »

Δx = (b-a)/n

Équation pour trouver xi

xi = a + iΔx

Identité trigo 1 (celle avec sin et cos)

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

Identité trigo 2 (celle avec sec et tan)

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

Identité trigo 3 (celle avec csc et cot)

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

Construction triangle sin

sinθ = O/H

Construction triangle cos

cosθ = A/H

Construction triangle tan

tanθ = O/A

Construction triangle csc

cscθ = H/O

Construction triangle sec

secθ = H/A

Construction triangle cot

cotθ = A/O