Lösung 1.2:1a

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Because the expression is a product of two factors, we use the product rule,
Because the expression is a product of two factors, we use the product rule,
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{{Displayed math||<math>\begin{align}
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{{Abgesetzte Formel||<math>\begin{align}
(\sin x\cdot\cos x)^{\prime }
(\sin x\cdot\cos x)^{\prime }
&= (\cos x)^{\prime }\cdot\sin x + \cos x\cdot (\sin x)^{\prime }\\[5pt]
&= (\cos x)^{\prime }\cdot\sin x + \cos x\cdot (\sin x)^{\prime }\\[5pt]

Version vom 12:51, 10. Mär. 2009

Because the expression is a product of two factors, we use the product rule,

\displaystyle \begin{align}

(\sin x\cdot\cos x)^{\prime } &= (\cos x)^{\prime }\cdot\sin x + \cos x\cdot (\sin x)^{\prime }\\[5pt] &= -\sin x\cdot\sin x + \cos x\cdot\cos x\\[5pt] &= -\sin^2\!x + \cos^2\!x\,\textrm{.} \end{align}

Using the formula for double angles, the answer can be simplified to \displaystyle \cos 2x\,.

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