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

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

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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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