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Lösung 1.1:2d

Aus Online Mathematik Brückenkurs 2

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K (Lösning 1.1:2d moved to Solution 1.1:2d: Robot: moved page)
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If we write
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<center> [[Image:1_1_2d.gif]] </center>
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<math>\sqrt{x}</math>
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in power form
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<math>x^{{1}/{2}\;}</math>, we see that the square root is a function having the appearance of
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<math>x^{n}</math>
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and its derivative is therefore equal to
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<math>{f}'\left( x \right)=\frac{d}{dx}\sqrt{x}=\frac{d}{dx}x^{{1}/{2}\;}=\frac{1}{2}x^{\frac{1}{2}-1}=\frac{1}{2}x^{-\frac{1}{2}}</math>
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The answer can also be written as
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<math>{f}'\left( x \right)=\frac{1}{2\sqrt{x}}</math>
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because
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<math>x^{-\frac{1}{2}}=\left( x^{\frac{1}{2}} \right)^{-1}=\left( \sqrt{x} \right)^{-1}=\frac{1}{\sqrt{x}}</math>

Version vom 11:30, 10. Okt. 2008

If we write x  in power form x12 , we see that the square root is a function having the appearance of xn and its derivative is therefore equal to


fx=ddxx=ddxx12=21x21−1=21x−21 

The answer can also be written as


fx=12x 


because x−21=x21−1=x−1=1x 

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_1.1:2d“