Correct Answer: Option C

Explanation

x = (2+3t)(5t-4)
Let u = 2+3t ∴ \(\frac{\text{du}}{\text{dt}}\) = 3
and v = 5t-4 ∴ \(\frac{\text{dv}}{\text{dt}}\) = 5
dx/dt = \(\frac{\text{Vdu}}{\text{dt}}\) + \(\frac{\text{Udv}}{\text{dt}}\)
= (5t-4)3 + (2+3t)5
= 15t - 12 + 10 + 15t
= 30t - 2
= 30 x \(\frac{4}{5}\) - 2
= 24 - 2
= 22

There is an explanation video available below.

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