Question

Asked Mar 7, 2019

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Find the first and second derivatives of the function.

(6*t*^{2} - 4)^{2} (5*t*^{2})

Step 1

Given function: f(t) = (6*t*^{2} - 4)^{2} (5*t*^{2}) = (36*t*^{4} - 48t^{2} + 16) (5*t*^{2}) = 180t^{6} - 240t^{4} + 80t^{2}

Recall the famous rule of differentiation: d(x^{n}) / dx = nx^{n-1}

Step 2

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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