Jambmaths question:
If $y=3\cos (\tfrac{x}{3})$find $\frac{dy}{dx}$when $x=\tfrac{3\pi }{2}$
Option A:
1
Option B:
–3
Option C:
2
Option D:
–1
Jamb Maths Solution:
\[\begin{align} & y=3\cos (\tfrac{x}{3}) \\ & \frac{dy}{dx}=-3\sin (\tfrac{x}{3})\times \tfrac{1}{3}=-\sin (\tfrac{x}{3}) \\ & \text{At }x=\frac{3\pi }{2}radian \\ & \frac{dy}{dx}\left| _{x=\tfrac{3\pi }{2}} \right.=-\sin \left( \frac{3\pi }{2\times 3} \right)=-\sin \left( \frac{\pi }{2} \right)=-1 \\ & Note:\frac{\pi }{2}radian={{45}^{o}} \\\end{align}\]
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