If s = (2 + 3t)(5t – 4), find ds/dt when t = 4/5 secs

Explanation

x = (2+3t)(5t-4)
Let u = 2+3t ∴du/dt = 3
and v = 5t-4 ∴dv/dt = 5
dx/dt = Vdu/dt + Udv/dt
= (5t-4)3 + (2+3t)5
= 15t - 12 + 10 + 15t
= 30t - 2
= 30x4/5 - 2
= 24 - 2
= 22

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