Solution 1.2:1a
From Förberedande kurs i matematik 2
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
.
