Solution 1.2:1a

From Förberedande kurs i matematik 2

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Because the expression is a product of two factors, we use the product rule:
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<center> [[Image:1_2_1a.gif]] </center>
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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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.

Revision as of 14:07, 12 September 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 .