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Catégorie :Category: nCreator TI-Nspire
Auteur Author: dissstt
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.51 Ko KB
Mis en ligne Uploaded: 20/07/2025 - 21:18:59
Uploadeur Uploader: dissstt (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4801859
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.51 Ko KB
Mis en ligne Uploaded: 20/07/2025 - 21:18:59
Uploadeur Uploader: dissstt (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4801859
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
<<
38.Problem 38 s = [(2 + 3i)/(2 3i)]. It's a constant Ò s' = 0. 39.Problem 39 y = (2px) = (2p x)^(1/2). Rewrite as (2p)·x^(1/2). y' = (2p)·½x^(1/2) = (2p)/(2x). 40.Problem 40 y = (b/a)(a^2 x^2). Rewrite: = (b/a)(a^2 x^2)^(1/2). y' = (b/a)·½(a^2 x^2)^(1/2)(2x) = (b x)/(a(a^2 x^2)). 41.Problem 41 y = (a^(2/3) x^(2/3))^(3/2). Let u = a^(2/3) x^(2/3); so y = u^(3/2). du/dx = (2/3)x^(1/3). dy/du = (3/2)u^(1/2). => y' = (3/2)u^(1/2)·[(2/3)x^(1/3)] = u^(1/2)x^(1/3) = (a^(2/3) x^(2/3))^(1/2)x^(1/3). 42.Problem 42 f(x) = (2x) + (3x) = (2x)^(1/2) + (3x)^(1/3). d/dx(2x)^(1/2) = 1/(2x). d/dx(3x)^(1/3) = (3x)^(2/3). So f' = 1/(2x) + (3x)^(2/3). 43.Problem 43 y = (2 x)/(1 + 2x^2). Using u = 2 x, v = 1 + 2x^2; u' = 1, v' = 4x. y' = [(1 + 2x^2)(1) (2 x)4x]/(1 + 2x^2)^2 = (1 8x + 2x^2)/(1 + 2x^2)^2. 44.Problem 44 y = x/(a bx) = x(a bx)^(1/2). u = x, v = (a bx)^(1/2); v' = b/2(a bx)^(3/2). y' = v + x·v' = (a bx)^(1/2) + (bx)/(2(a bx)^(3/2)). 45.Problem 45 s = (a + bt)/t = (a + bt)^(1/2)t^(1). u = (a + bt)^(1/2), v = t^(1). u' = b/2(a + bt)^(1/2), v' = t^(2). s' = u'v + uv' = [b/(2t(a + bt))] [(a + bt)/t^2]. 46 r = (a + b¸)/¸ = (a + b¸)^(1/3)¸^(1). u = (a + b¸)^(1/3), v = ¸^(1). u' = b/3(a + b¸)^(2/3), v' = ¸^(2). r' = u'v + uv' = [b/(3¸(a + b¸)^(2/3))] [(a + b¸)^(1/3)/¸^2]. 47 y = x^2(5 2x) = x^2(5 2x)^(1/2). u = x^2, v = (5 2x)^(1/2); u' = 2x, v' = 1/((5 2x)). y' = u'v + uv' = 2x(5 2x) [x^2/(5 2x)]. 48 y = x(2 + 3x) = x(2 + 3x)^(1/3). u = x, v = (2 + 3x)^(1/3); u' = 1, v' = (2 + 3x)^(2/3). y' = v + x·v' = (2 + 3x)^(1/3) + x(2 + 3x)^(2/3). 49 s = (2t t^(2)) = [2t t^(2)]^(1/2). u = 2t t^(2), u' = 2 + 2t^(3). s' = ½u^(1/2)·u' = [1 + t^(3)]/(2t 1/t^2). 50 y = (x + 2)^2(x^2 + 2) = (x + 2)^2(x^2 + 2)^(1/2). u = (x + 2)^2, u' = 2(x + 2); v = (x^2 + 2), v' = x/(x^2 + 2). y' = u'v + uv' = 2(x + 2)(x^2 + 2) + [x(x + 2)^2/(x^2 + 2)]. 51 y = (1 + 2x)/(1 + 3x) = (1 + 2x)^(1/2)(1 + 3x)^(1/3). u = (1 + 2x)^(1/2), u' = 1/(1 + 2x); v = (1 + 3x)^(1/3), v' = (1 + 3x)^(4/3). y' = u'v + uv' = [(1 + 3x)^(1/3)/(1 + 2x)] [(1 + 2x)^(1/2)(1 + 3x)^(4/3)]. Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
38.Problem 38 s = [(2 + 3i)/(2 3i)]. It's a constant Ò s' = 0. 39.Problem 39 y = (2px) = (2p x)^(1/2). Rewrite as (2p)·x^(1/2). y' = (2p)·½x^(1/2) = (2p)/(2x). 40.Problem 40 y = (b/a)(a^2 x^2). Rewrite: = (b/a)(a^2 x^2)^(1/2). y' = (b/a)·½(a^2 x^2)^(1/2)(2x) = (b x)/(a(a^2 x^2)). 41.Problem 41 y = (a^(2/3) x^(2/3))^(3/2). Let u = a^(2/3) x^(2/3); so y = u^(3/2). du/dx = (2/3)x^(1/3). dy/du = (3/2)u^(1/2). => y' = (3/2)u^(1/2)·[(2/3)x^(1/3)] = u^(1/2)x^(1/3) = (a^(2/3) x^(2/3))^(1/2)x^(1/3). 42.Problem 42 f(x) = (2x) + (3x) = (2x)^(1/2) + (3x)^(1/3). d/dx(2x)^(1/2) = 1/(2x). d/dx(3x)^(1/3) = (3x)^(2/3). So f' = 1/(2x) + (3x)^(2/3). 43.Problem 43 y = (2 x)/(1 + 2x^2). Using u = 2 x, v = 1 + 2x^2; u' = 1, v' = 4x. y' = [(1 + 2x^2)(1) (2 x)4x]/(1 + 2x^2)^2 = (1 8x + 2x^2)/(1 + 2x^2)^2. 44.Problem 44 y = x/(a bx) = x(a bx)^(1/2). u = x, v = (a bx)^(1/2); v' = b/2(a bx)^(3/2). y' = v + x·v' = (a bx)^(1/2) + (bx)/(2(a bx)^(3/2)). 45.Problem 45 s = (a + bt)/t = (a + bt)^(1/2)t^(1). u = (a + bt)^(1/2), v = t^(1). u' = b/2(a + bt)^(1/2), v' = t^(2). s' = u'v + uv' = [b/(2t(a + bt))] [(a + bt)/t^2]. 46 r = (a + b¸)/¸ = (a + b¸)^(1/3)¸^(1). u = (a + b¸)^(1/3), v = ¸^(1). u' = b/3(a + b¸)^(2/3), v' = ¸^(2). r' = u'v + uv' = [b/(3¸(a + b¸)^(2/3))] [(a + b¸)^(1/3)/¸^2]. 47 y = x^2(5 2x) = x^2(5 2x)^(1/2). u = x^2, v = (5 2x)^(1/2); u' = 2x, v' = 1/((5 2x)). y' = u'v + uv' = 2x(5 2x) [x^2/(5 2x)]. 48 y = x(2 + 3x) = x(2 + 3x)^(1/3). u = x, v = (2 + 3x)^(1/3); u' = 1, v' = (2 + 3x)^(2/3). y' = v + x·v' = (2 + 3x)^(1/3) + x(2 + 3x)^(2/3). 49 s = (2t t^(2)) = [2t t^(2)]^(1/2). u = 2t t^(2), u' = 2 + 2t^(3). s' = ½u^(1/2)·u' = [1 + t^(3)]/(2t 1/t^2). 50 y = (x + 2)^2(x^2 + 2) = (x + 2)^2(x^2 + 2)^(1/2). u = (x + 2)^2, u' = 2(x + 2); v = (x^2 + 2), v' = x/(x^2 + 2). y' = u'v + uv' = 2(x + 2)(x^2 + 2) + [x(x + 2)^2/(x^2 + 2)]. 51 y = (1 + 2x)/(1 + 3x) = (1 + 2x)^(1/2)(1 + 3x)^(1/3). u = (1 + 2x)^(1/2), u' = 1/(1 + 2x); v = (1 + 3x)^(1/3), v' = (1 + 3x)^(4/3). y' = u'v + uv' = [(1 + 3x)^(1/3)/(1 + 2x)] [(1 + 2x)^(1/2)(1 + 3x)^(4/3)]. Made with nCreator - tiplanet.org
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