1.2 Übungen
Aus Online Mathematik Brückenkurs 2
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|width="33%"| <math>\displaystyle\frac{x \ln x}{\sin x}</math> | |width="33%"| <math>\displaystyle\frac{x \ln x}{\sin x}</math> | ||
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| - | </div>{{#NAVCONTENT:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 1.2:1|Solution a|Lösning 1.2:1a|Solution b|Lösning 1.2:1b|Solution c|Lösning 1.2:1c|Solution d|Lösning 1.2:1d|Solution e|Lösning 1.2:1e|Solution f|Lösning 1.2:1f}} |
===Example 1.2:2=== | ===Example 1.2:2=== | ||
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|width="33%"| <math>\cos \sqrt{1-x}</math> | |width="33%"| <math>\cos \sqrt{1-x}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 1.2:2|Solution a|Lösning 1.2:2a|Solution b|Lösning 1.2:2b|Solution c|Lösning 1.2:2c|Solution d|Lösning 1.2:2d|Solution e|Lösning 1.2:2e|Solution f|Lösning 1.2:2f}} |
===Example 1.2:3=== | ===Example 1.2:3=== | ||
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|width="33%"| <math>x^{\tan x}</math> | |width="33%"| <math>x^{\tan x}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 1.2:3|Solution a|Lösning 1.2:3a|Solution b|Lösning 1.2:3b|Solution c|Lösning 1.2:3c|Solution d|Lösning 1.2:3d|Solution e|Lösning 1.2:3e|Solution f|Lösning 1.2:3f}} |
===Example 1.2:4=== | ===Example 1.2:4=== | ||
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|width="50%"| <math>x ( \sin \ln x +\cos \ln x )</math> | |width="50%"| <math>x ( \sin \ln x +\cos \ln x )</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 1.2:4|Solution a|Lösning 1.2:4a|Solution b|Lösning 1.2:4b}} |
Version vom 14:12, 16. Sep. 2008
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Example 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} |
Answer
Laden...
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Example 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} |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Example 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} |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Example 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 ) |
