Lösung 1.2:1b
Aus Online Mathematik Brückenkurs 2
(Unterschied zwischen Versionen)
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We use the product rule with <math>x^2</math> and <math>\ln x</math> as factors, | We use the product rule with <math>x^2</math> and <math>\ln x</math> as factors, | ||
| - | {{ | + | {{Abgesetzte Formel||<math>\begin{align} |
\bigl(x^{2}\ln x\bigr)' | \bigl(x^{2}\ln x\bigr)' | ||
&= \bigl(x^2\bigr)'\,\ln x + x^2\,(\ln x)'\\[5pt] | &= \bigl(x^2\bigr)'\,\ln x + x^2\,(\ln x)'\\[5pt] | ||
Version vom 12:52, 10. Mär. 2009
We use the product rule with \displaystyle x^2 and \displaystyle \ln x as factors,
| \displaystyle \begin{align}
\bigl(x^{2}\ln x\bigr)' &= \bigl(x^2\bigr)'\,\ln x + x^2\,(\ln x)'\\[5pt] &= 2x\cdot\ln x + x^2\cdot\frac{1}{x}\\[5pt] &= 2x\ln x + x\,\textrm{.} \end{align} |
