1.2 Übungen
Aus Online Mathematik Brückenkurs 2
| Theory | Examples |
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
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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 ) |
