Question 37

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Jambmaths question: 

If $s=(2+3t)(5t-4),\text{ find }\frac{ds}{dt}$ when t = $\tfrac{4}{5}$secs.

Jamb Maths Solution: 

$\begin{align}  & s=(2+3t)(5t-4) \\ & \text{Applying the product rule} \\ & \frac{ds}{dt}=(2+3t)\tfrac{d}{dt}(5t-4)+(5t-4)\tfrac{d}{dt}(2+3t) \\ & \frac{ds}{dt}=(2+3t)(5)+(5t-4)(3) \\ & \frac{ds}{dt}=10+15t+15t-12=30t-2 \\ & \text{when }t=\tfrac{4}{5}s \\ & \frac{ds}{dt}\left| _{t=\tfrac{4}{5}s} \right.=30(\tfrac{4}{5})-2=22\text{ }units\text{ }per\sec  \\\end{align}$

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