Question 28.7.8: Differentiate sin 2x cos 3x ....
Differentiate \sin 2 x \cos 3 x .
Step-by-Step
By using the product rule, we have
\begin{aligned}\frac{d}{d x}(\sin 2 x \cos 3 x) & =(\sin 2 x) \cdot \frac{d}{d x}(\cos 3 x)+(\cos 3 x) \cdot \frac{d}{d x}(\sin 2 x)\\ \\& =(\sin 2 x) \cdot(-\sin 3 x) \cdot 3+(\cos 3 x) \cdot(\cos 2 x) \cdot 2 \\ \\&\text{[using chain rule]}\\ \\& =(-3 \sin 2 x \sin 3 x+2 \cos 3 x \cos 2 x) .\end{aligned}
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