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)#