[PDF] Tableaux des dérivées

Tableaux des dérivées

cosh(x) R sinh(x) sinh(x) R cosh(x) tanh(x) R 1 tanh2(x) = 1 cosh2(x) arcosh(x) ]1;+1[1 p x2 1 arsinh(x) R 1 p x2 +1 artanh(x) ] 1;1[1 1 x2 Opération Dérivée f+g f0+g0 fg f0g+fg0 f g f0g fg0 g2 g f f0 g0 f (fg)(n) Xn k=0 n k f(k)g(n k) f 1 0 1 f0 1 1 u u0 u2 u ; 2R u0u 1 p u u0 2 p u ln(u) u0 u exp(u) u0exp(u) cos(u) u0sin(u) sin(u) u0cos(u) 1

Derivation of the formulas for cosh(x) and sinh(x)

Derivation of the formulas for cosh(x) and sinh(x)1 Let u be the area of the region OAB in Figure 1 Here O is the origin (0,0) The curve is the unit hyperbola x 2− y = 1 The points A and B have the same x coordinates and are the same distance from the x-axis Let their coordinates be denoted (c(u),s(u)) and (c(u),−s(u)), respectively

26 Derivatives of Trigonometric and HyperbolicFunctions

(x,y) = (cosh t, sinh t) x y Now let’s consider the path traced out by the hyperbola x 2−y =1as shown above right One parameterizationof the right half of this hyperbola is traced out by the hyperbolic func-tions (cosht,sinht) that we will spend the rest of this section investigating

Derivation of the Inverse Hyperbolic Trig Functions

y =cosh−1 x By definition of an inverse function, we want a function that satisfies the condition x =coshy e y+e− 2 by definition of coshy e y+e−y 2 e ey e2y +1 2ey 2eyx = e2y +1 e2y −2xey +1 = 0

Deriving the Hyperbolic Trig Functions - Isaac Greenspan

()cosh x Part IV The Other Hyperbolic Trig Functions Since sinh and cosh are defined in a analogous manner to sine and cosine, we can quite logically define four more hyperbolic functions as follows: sinh tanh cosh x x x = cosh coth sinh x x x = 1 sech cosh x x = 1 csch sinh x x = Using the quotient rule along with your results from Part III

Section 69, The Hyperbolic Functions and Their Inverses

sinh and cosh satisfy the identity cosh2 x sinh2 x = 1: We can see this by writing it out: cosh2 x sinh2 x = e2x + 2 + e 2x 2 e2x 2 + e 2x 2 = 1: Note that sinh is an odd function since sinh( x) = sinhx and cosh is an even function since cosh( x) = coshx The graphs of four of these functions are shown in Figure 3 on page 375 of the book (also

Eagleworks Laboratories WARP FIELD MECHANICS 102: Energy

Trivially, the Lorentz Transform or boost field is: cosh( ) Boost Field: 2 2 2 2 2 2 2 2 2 ( ) 1 ( ) ( ) 1 dx dy dz v f r v f r ds v f r dt s s s s s s ds2 2 dx v f (r)dt dy2 dz2 s s Dr Harold “Sonny” White 06/23/2011 Dr Harold “Sonny” White 09/02/2011 28

La trigonométrie des figures et formes géométriques arrondies

cosh O ( T) (4 6) ℎ ( T)= ( T) ( T) = cosh O ( T) sinh O ( T) (4 7) V- Généralisation des fonctions trigonométriques symétriques Nous définissons les fonctions trigonométriques symétriques comme toutes formules qui satisfont l’équation T + U =1 où I=2 G, G de , les fonctions

Warp Field Mechanics 101 Dr Harold “Sonny” White NASA

MPSI 1 Formulaire de mathématiques Trigonométrie circulaire

MPSI 1 Formulaire de mathématiques Développements limités 4 Développements limités Formule de Taylor-Young Si la fonction f est définie, continue et pourvue de dérivées successives jusqu'à l'ordre n sur un intervalle I comprenant x0, le