Lösung 1.2:1a

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Because the expression is a product of two factors, we use the product rule:
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<math>\begin{align}
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& \left( \sin x\centerdot \cos x \right)^{\prime }=\left( \cos x \right)^{\prime }\centerdot \sin x+\cos x\centerdot \left( \sin x \right)^{\prime } \\
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& \\
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& =-\sin x\centerdot \sin x+\cos x\centerdot \cos x=\sin ^{2}x+\cos ^{2}x \\
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\end{align}</math>
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Using the formula for double angles, the answer can be simplified to
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<math>\cos 2x</math>
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Version vom 14:07, 12. Sep. 2008

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


\displaystyle \begin{align} & \left( \sin x\centerdot \cos x \right)^{\prime }=\left( \cos x \right)^{\prime }\centerdot \sin x+\cos x\centerdot \left( \sin x \right)^{\prime } \\ & \\ & =-\sin x\centerdot \sin x+\cos x\centerdot \cos x=\sin ^{2}x+\cos ^{2}x \\ \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“