Posted by Jake on Tuesday, February 5, 2013 at 12:51am.
find the derivatives of the given functions.
g(t)=sqrt t(1+t)/t^2

calc  Steve, Tuesday, February 5, 2013 at 5:20am
Is that √ everything, or
√(t(1+t)) / t^2, or
(√t)(1+t)/t^2 ?

calc  Steve, Tuesday, February 5, 2013 at 5:39am
Ah, I see from a prior post, we have
g(t) = √t (1+t)/t^2
you can expand that to be
g(t) = t^(3/2) + t^(1/2)
so the derivative is trivial:
g'(t) = 3/2 t^(5/2)  1/2 t^(3/2)
= (3+t) / (t^2 √t)
or you can use the product rule to get
g'(t) = 1/2√t (1+t)/t^2 + √t (1)/t^2  2√t (1+t)/t^3
= (1+t)/2t^2√t + 2t/2t^2√t  (4+4t)/2t^2√t
= (1+t+2t44t)/2t^2√t
= (3+t)/2t^2√t

calc  find the typo  Steve, Tuesday, February 5, 2013 at 5:40am
find the typo so the two solutions agree!

calc  Jake, Tuesday, February 5, 2013 at 9:16am
agree thank you steve
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