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How do you differentiate g(t)= t(4-t)^1/2?````

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marast | eNotes Newbie

Posted July 27, 2013 at 8:26 PM via web

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How do you differentiate g(t)= t(4-t)^1/2?````

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llltkl | College Teacher | (Level 3) Valedictorian

Posted July 28, 2013 at 2:29 AM (Answer #1)

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Given `g(t) = t(4-t)^(1/2)`

Using the product rule:

`g'(t) = (4-t)^(1/2)*1+t*1/2*(4-t)^(-1/2)*-1`

`g'(t) = (4-t)^(1/2)-(t (4-t)^(-1/2)) / 2`

`g'(t) = sqrt(4-t)-t/(2 sqrt(4-t))` `rarr` answer.

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