1.2 Übungen
Aus Online Mathematik Brückenkurs 2
(Unterschied zwischen Versionen)
K (Robot: Automated text replacement (-Solution +Lösung)) |
K (Robot: Automated text replacement (-Example +Beispiel)) |
||
| Zeile 3: | Zeile 3: | ||
| style="border-bottom:1px solid #000" width="5px" | | | style="border-bottom:1px solid #000" width="5px" | | ||
{{Not selected tab|[[1.2 Ableitungsregeln|Theorie]]}} | {{Not selected tab|[[1.2 Ableitungsregeln|Theorie]]}} | ||
| - | {{Selected tab|[[1.2 Übungen| | + | {{Selected tab|[[1.2 Übungen|Beispiels]]}} |
| style="border-bottom:1px solid #000" width="100%"| | | style="border-bottom:1px solid #000" width="100%"| | ||
|} | |} | ||
| - | === | + | ===Beispiel 1.2:1=== |
<div class="ovning"> | <div class="ovning"> | ||
Calculate the derivative of the following functions and write the answer in simplest possible form: | Calculate the derivative of the following functions and write the answer in simplest possible form: | ||
| Zeile 27: | Zeile 27: | ||
</div>{{#NAVCONTENT:Antwort|Antwort 1.2:1|Lösung a|Lösung 1.2:1a|Lösung b|Lösung 1.2:1b|Lösung c|Lösung 1.2:1c|Lösung d|Lösung 1.2:1d|Lösung e|Lösung 1.2:1e|Lösung f|Lösung 1.2:1f}} | </div>{{#NAVCONTENT:Antwort|Antwort 1.2:1|Lösung a|Lösung 1.2:1a|Lösung b|Lösung 1.2:1b|Lösung c|Lösung 1.2:1c|Lösung d|Lösung 1.2:1d|Lösung e|Lösung 1.2:1e|Lösung f|Lösung 1.2:1f}} | ||
| - | === | + | ===Beispiel 1.2:2=== |
<div class="ovning"> | <div class="ovning"> | ||
Calculate the derivative of the following functions and write the answer in simplest possible form: | Calculate the derivative of the following functions and write the answer in simplest possible form: | ||
| Zeile 47: | Zeile 47: | ||
</div>{{#NAVCONTENT:Antwort|Antwort 1.2:2|Lösung a|Lösung 1.2:2a|Lösung b|Lösung 1.2:2b|Lösung c|Lösung 1.2:2c|Lösung d|Lösung 1.2:2d|Lösung e|Lösung 1.2:2e|Lösung f|Lösung 1.2:2f}} | </div>{{#NAVCONTENT:Antwort|Antwort 1.2:2|Lösung a|Lösung 1.2:2a|Lösung b|Lösung 1.2:2b|Lösung c|Lösung 1.2:2c|Lösung d|Lösung 1.2:2d|Lösung e|Lösung 1.2:2e|Lösung f|Lösung 1.2:2f}} | ||
| - | === | + | ===Beispiel 1.2:3=== |
<div class="ovning"> | <div class="ovning"> | ||
Calculate the derivative of the following functions and write the answer in simplest possible form: | Calculate the derivative of the following functions and write the answer in simplest possible form: | ||
| Zeile 67: | Zeile 67: | ||
</div>{{#NAVCONTENT:Antwort|Antwort 1.2:3|Lösung a|Lösung 1.2:3a|Lösung b|Lösung 1.2:3b|Lösung c|Lösung 1.2:3c|Lösung d|Lösung 1.2:3d|Lösung e|Lösung 1.2:3e|Lösung f|Lösung 1.2:3f}} | </div>{{#NAVCONTENT:Antwort|Antwort 1.2:3|Lösung a|Lösung 1.2:3a|Lösung b|Lösung 1.2:3b|Lösung c|Lösung 1.2:3c|Lösung d|Lösung 1.2:3d|Lösung e|Lösung 1.2:3e|Lösung f|Lösung 1.2:3f}} | ||
| - | === | + | ===Beispiel 1.2:4=== |
<div class="ovning"> | <div class="ovning"> | ||
Calculate the second derivative of the following functions and write the answer in simplest possible form: | Calculate the second derivative of the following functions and write the answer in simplest possible form: | ||
Version vom 13:35, 10. Mär. 2009
| Theorie | Beispiels |
Beispiel 1.2:1
Calculate the derivative of the following functions and write the answer in simplest possible form:
| a) | \displaystyle \cos x \cdot \sin x | b) | \displaystyle x^2\ln x | c) | \displaystyle \displaystyle\frac{x^2+1}{x+1} |
| d) | \displaystyle \displaystyle\frac{\sin x}{x} | e) | \displaystyle \displaystyle\frac{x}{\ln x} | f) | \displaystyle \displaystyle\frac{x \ln x}{\sin x} |
Antwort
Laden...
Lösung a
Lösung b
Lösung c
Lösung d
Lösung e
Lösung f
Beispiel 1.2:2
Calculate the derivative of the following functions and write the answer in simplest possible form:
| a) | \displaystyle \sin x^2 | b) | \displaystyle e^{x^2+x} | c) | \displaystyle \sqrt{\cos x} |
| d) | \displaystyle \ln \ln x | e) | \displaystyle x(2x+1)^4 | f) | \displaystyle \cos \sqrt{1-x} |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Lösung e
Lösung f
Beispiel 1.2:3
Calculate the derivative of the following functions and write the answer in simplest possible form:
| a) | \displaystyle \ln (\sqrt{x} + \sqrt{x+1}\,) | b) | \displaystyle \sqrt{\displaystyle \frac{x+1}{x-1}} | c) | \displaystyle \displaystyle\frac{1}{x\sqrt{1-x^2}} |
| d) | \displaystyle \sin \cos \sin x | e) | \displaystyle e^{\sin x^2} | f) | \displaystyle x^{\tan x} |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Lösung e
Lösung f
Beispiel 1.2:4
Calculate the second derivative of the following functions and write the answer in simplest possible form:
| a) | \displaystyle \displaystyle\frac{x}{\sqrt{1-x^2}} | b) | \displaystyle x ( \sin \ln x +\cos \ln x ) |
