Find the first and second derivatives of the function.
(6t2 - 4)2 (5t2)
Given function: f(t) = (6t2 - 4)2 (5t2) = (36t4 - 48t2 + 16) (5t2) = 180t6 - 240t4 + 80t2
Recall the famous rule of differentiation: d(xn) / dx = nxn-1
First derivative = f'(t) = df(t) / dt = 180 x 6 x t5 - 240 x 4 x t3 + 80 x 2 x t = 1,080t5 - 960t3 + 160t
Second derivative = f''(t) = d2f(t)...
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