Processing Math: Done
Lösung 1.1:2a
Aus Online Mathematik Brückenkurs 2
(Unterschied zwischen Versionen)
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By using the rule for differentiation | By using the rule for differentiation | ||
+ | {{Displayed math||<math>\frac{d}{dx}\,x^{n}=nx^{n-1}</math>}} | ||
- | + | and the fact that the expression can be differentiated term by term and that constant factors can be taken outside the differentiation, we obtain | |
- | + | {{Displayed math||<math>\begin{align} | |
- | + | f^{\,\prime}(x) &= \frac{d}{dx}\,\bigl(x^2-3x+1\bigr)\\[5pt] | |
- | + | &= \frac{d}{dx}\,x^2 - 3\frac{d}{dx}\,x^1 + \frac{d}{dx}\,1\\[5pt] | |
- | + | &= 2x^{2-1} - 3\cdot 1x^{1-1} + 0\\[5pt] | |
- | <math>\begin{align} | + | &= 2x-3\,\textrm{.} |
- | + | \end{align}</math>}} | |
- | & =2x^{2-1}-3\ | + | |
- | \end{align}</math> | + |
Version vom 11:45, 14. Okt. 2008
By using the rule for differentiation
and the fact that the expression can be differentiated term by term and that constant factors can be taken outside the differentiation, we obtain
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