If \( x = \sin t - \cos t \) and \( y = \sin t \cos t \), find the value of \(\frac{dy}{dx}\) evaluated at \( t = \frac{\pi}{4} \).
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Always simplify using trigonometric double angle formulas before differentiating. It saves huge amounts of time compared to doing product rules. For example, rewriting \( y = \frac{1}{2}\sin 2t \) directly gave us \(\cos 2t\) as the derivative in a single line!