Ableitung < Trigonometr. Fktn < Analysis < Oberstufe < Schule < Mathe < Vorhilfe
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(Frage) beantwortet  | | Datum: | 18:23 Mo 02.11.2009 | | Autor: | Dinker |
Hallo
g(t) = [mm] cos^2 [/mm] (2t) * tan (2t)
= [mm] cos^2 [/mm] (2t) * [mm] \bruch{sin (2t)}{cos (2t)}
[/mm]
= cos (2t) * sin (2t)
u = cos (2t) u' = -2 sin (2t)
v = sin (2t) v' = 2 cos (2t)
g'(t) = cos (2t) * 2 cos (2t) + sin (2t) * -(2 sin (2t))
2 [mm] cos^2 [/mm] (2t) - 2 [mm] sin^2 [/mm] (2t)
= 2 cos (2t) - 2*(1 - [mm] cos^2 [/mm] (2t))
= 2 cos (2t) - 2 + 2 [mm] cos^2 [/mm] (2t)
Was mache ich falsch?
Danke
Gruss Dinker
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(Antwort) fertig  | | Datum: | 18:36 Mo 02.11.2009 | | Autor: | Loddar |
Hallo Dinker!
> 2 [mm]cos^2[/mm] (2t) - 2 [mm]sin^2[/mm] (2t)
![[ok]](/images/smileys/ok.gif "[ok]")
> = 2 cos (2t) - 2*(1 - [mm]cos^2[/mm] (2t))
Du unterschlägst hier beim ersten Cosinusterm plötzlich das Quadrat.
Gruß
Loddar
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