How do you differentiate $(t-2)^3 (t-6)$ ?

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Answer 1 · 2016-10-31T20:14:59

see below

$f(t)=(t-2)^3 (t-6)$

Use product rule $(fg)'=fg'+gf'$

$f = (t-2)^3, g=t-6$

$f'=3(t-2)^2*1 , g' = 1$

$f'(t)=(t-2)^3+3(t-2)^2(t-6)$

$f'(t)=(t-2)^2[t-2+3(t-6)]$

$f'(t)=(t-2)^2[t-2+3t-18]$

$f'(t)=(t-2)^2(4t-20)$

How do you differentiate (t-2)^3 (t-6)(t-2)^3 (t-6)?