Solution 1.2:1b
From Förberedande kurs i matematik 2
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| - | {{ | + | We use the product rule with <math>x^2</math> and <math>\ln x</math> as factors, |
| - | + | ||
| - | {{ | + | {{Displayed math||<math>\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}</math>}} | ||
Current revision
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} |
