10-37
DownloadTélécharger
Actions
Vote :
ScreenshotAperçu
Informations
Catégorie :Category: nCreator TI-Nspire
Auteur Author: dissstt
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.90 Ko KB
Mis en ligne Uploaded: 20/07/2025 - 21:18:57
Uploadeur Uploader: dissstt (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4801858
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.90 Ko KB
Mis en ligne Uploaded: 20/07/2025 - 21:18:57
Uploadeur Uploader: dissstt (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4801858
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
<<
10.Differentiate d/dx (4 + 3x 2x^3). Termbyterm: d(4)/dx = 0, d(3x)/dx = 3, d(2x^3)/dx = 6x^2. Result: d/dx (&) = 3 6x^2. 11.Differentiate d/dt (a t^5 0.5 b t^3). d(a t^5)/dt = 5 a t^4, d(0.5 b t^3)/dt = 1.5 b t^2. Hence: d/dt (&) = 5a t^4 1.5b t^2. 12.Differentiate d/dz (z^2/2 z^7/7). d(z^2/2)/dz = z, d(z^7/7)/dz = z^6. So: d/dz (&) = z z^6. 13.Differentiate d/dx v. Assuming v = v(x): d/dx v = (1 / 2v) · dv/dx. If v = x: d/dx x = 1 / (2x). 14.Differentiate d/dx (2/x 3/x^2). Rewrite: 2x^(1) 3x^(2). d(2x^(1))/dx = 2x^(2), d(3x^(2))/dx = 6x^(3). So: d/dx (&) = 2/x^2 + 6/x^3. 15.Differentiate d/dt (2t^(4/3) 3t^(2/3)). d(2t^(4/3))/dt = (8/3)t^(1/3), d(3t^(2/3))/dt = 2t^(1/3). Result: = (8/3)t^(1/3) 2t^(1/3). 16.Differentiate d/dx (2x^(3/4) + 4x^(1/4)). d(2x^(3/4))/dx = (3/2)x^(1/4), d(4x^(1/4))/dx = x^(5/4). Hence: = (3/2)x^(1/4) x^(5/4). 17.Differentiate d/dx (x^(3/3) a^(3/3)). Since x^(3/3)=x, a^(3/3)=a: d/dx = 1 0 = 1. 18.Differentiate d/dx ((a + b x + c x^2)/x). Rewrite = a/x + b + c x: d(a/x)/dx = a/x^2, d(b)=0, d(cx)=c. => = c a/x^2. 19.Differentiate y = x/2 2/x. Rewrite y = ½x^(1/2) 2x^(1/2). d(...) = ¼x^(1/2) + x^(3/2). 20.Differentiate s = (a + b t + c t^2)/t. Rewrite s = a t^(1/2) + b t^(1/2) + c t^(3/2). d/dt: = (a/2)t^(3/2) + (b/2)t^(1/2) + (3c/2)t^(1/2). 21.Differentiate y = (ax) + a/(ax). Rewrite: y = a (x^(1/2) + x^(1/2)). d/dx: y' = (a/2)(x^(1/2) x^(3/2)). 22.Differentiate r = (1 2¸). r' = 1 / (1 2¸). 23.Differentiate f(t) = (2 3t^2)^3. Let u=23t^2 => f = u^3. du/dt = 6t, df/du = 3u^2 => f' = 18t(2 3t^2)^2. 24.Differentiate F(x) = ³(4 9x). F' = 3 (4 9x)^(2/3). 25.Differentiate y = 1/(a^2 x^2). y' = x/(a^2 x^2)^(3/2). 26.Differentiate f(¸) = (2 5¸)^(3/5). f' = 3(2 5¸)^(2/5). 27.Differentiate y = (a b/x)^2. Let u = a b/x => du/dx = b/x^2; y' = 2u·(b/x^2) = (2b/x^2)(a b/x). 32.Differentiate y = (a^2 + x^2)/(a^2 x^2). u=a^2+x^2, v=a^2x^2 => u'=2x, v'=2x. y' = 4a^2 x/(a^2 x^2)^2. 33.Differentiate y = (a^2 + x^2)/x. y' = 1/(a^2 + x^2) (a^2 + x^2)/x^2. 34.Differentiate y = x/(a^2 x^2). y' = a^2/(a^2 x^2)^(3/2). 35.Differentiate r = ¸^2(3 4¸). r' = 2¸(3 4¸) (2¸^2)/(3 4¸). Alternative factor: r' = (2¸(3 5¸))/(3 4¸). 36.Differentiate y = ((1 c x)/(1 + c x)). y' = [c / (1 c^2 x^2)]((1 c x)/(1 + c x)). 37.Differentiate y = ((a^2 + x^2)/(a^2 x^2)). y' = y·x·[1/(a^2 + x^2) + 1/(a^2 x^2)]. Made with nCreator - tiplanet.org
>>
Compatible OS 3.0 et ultérieurs.
<<
10.Differentiate d/dx (4 + 3x 2x^3). Termbyterm: d(4)/dx = 0, d(3x)/dx = 3, d(2x^3)/dx = 6x^2. Result: d/dx (&) = 3 6x^2. 11.Differentiate d/dt (a t^5 0.5 b t^3). d(a t^5)/dt = 5 a t^4, d(0.5 b t^3)/dt = 1.5 b t^2. Hence: d/dt (&) = 5a t^4 1.5b t^2. 12.Differentiate d/dz (z^2/2 z^7/7). d(z^2/2)/dz = z, d(z^7/7)/dz = z^6. So: d/dz (&) = z z^6. 13.Differentiate d/dx v. Assuming v = v(x): d/dx v = (1 / 2v) · dv/dx. If v = x: d/dx x = 1 / (2x). 14.Differentiate d/dx (2/x 3/x^2). Rewrite: 2x^(1) 3x^(2). d(2x^(1))/dx = 2x^(2), d(3x^(2))/dx = 6x^(3). So: d/dx (&) = 2/x^2 + 6/x^3. 15.Differentiate d/dt (2t^(4/3) 3t^(2/3)). d(2t^(4/3))/dt = (8/3)t^(1/3), d(3t^(2/3))/dt = 2t^(1/3). Result: = (8/3)t^(1/3) 2t^(1/3). 16.Differentiate d/dx (2x^(3/4) + 4x^(1/4)). d(2x^(3/4))/dx = (3/2)x^(1/4), d(4x^(1/4))/dx = x^(5/4). Hence: = (3/2)x^(1/4) x^(5/4). 17.Differentiate d/dx (x^(3/3) a^(3/3)). Since x^(3/3)=x, a^(3/3)=a: d/dx = 1 0 = 1. 18.Differentiate d/dx ((a + b x + c x^2)/x). Rewrite = a/x + b + c x: d(a/x)/dx = a/x^2, d(b)=0, d(cx)=c. => = c a/x^2. 19.Differentiate y = x/2 2/x. Rewrite y = ½x^(1/2) 2x^(1/2). d(...) = ¼x^(1/2) + x^(3/2). 20.Differentiate s = (a + b t + c t^2)/t. Rewrite s = a t^(1/2) + b t^(1/2) + c t^(3/2). d/dt: = (a/2)t^(3/2) + (b/2)t^(1/2) + (3c/2)t^(1/2). 21.Differentiate y = (ax) + a/(ax). Rewrite: y = a (x^(1/2) + x^(1/2)). d/dx: y' = (a/2)(x^(1/2) x^(3/2)). 22.Differentiate r = (1 2¸). r' = 1 / (1 2¸). 23.Differentiate f(t) = (2 3t^2)^3. Let u=23t^2 => f = u^3. du/dt = 6t, df/du = 3u^2 => f' = 18t(2 3t^2)^2. 24.Differentiate F(x) = ³(4 9x). F' = 3 (4 9x)^(2/3). 25.Differentiate y = 1/(a^2 x^2). y' = x/(a^2 x^2)^(3/2). 26.Differentiate f(¸) = (2 5¸)^(3/5). f' = 3(2 5¸)^(2/5). 27.Differentiate y = (a b/x)^2. Let u = a b/x => du/dx = b/x^2; y' = 2u·(b/x^2) = (2b/x^2)(a b/x). 32.Differentiate y = (a^2 + x^2)/(a^2 x^2). u=a^2+x^2, v=a^2x^2 => u'=2x, v'=2x. y' = 4a^2 x/(a^2 x^2)^2. 33.Differentiate y = (a^2 + x^2)/x. y' = 1/(a^2 + x^2) (a^2 + x^2)/x^2. 34.Differentiate y = x/(a^2 x^2). y' = a^2/(a^2 x^2)^(3/2). 35.Differentiate r = ¸^2(3 4¸). r' = 2¸(3 4¸) (2¸^2)/(3 4¸). Alternative factor: r' = (2¸(3 5¸))/(3 4¸). 36.Differentiate y = ((1 c x)/(1 + c x)). y' = [c / (1 c^2 x^2)]((1 c x)/(1 + c x)). 37.Differentiate y = ((a^2 + x^2)/(a^2 x^2)). y' = y·x·[1/(a^2 + x^2) + 1/(a^2 x^2)]. Made with nCreator - tiplanet.org
>>
