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find the derivatives of the given functions.
g(t)=sqrt t(1+t)/t^2

  • calc -

    Is that √ everything, or
    √(t(1+t)) / t^2, or
    (√t)(1+t)/t^2 ?

  • calc -

    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+2t-4-4t)/2t^2√t
    = -(3+t)/2t^2√t

  • calc - find the typo -

    find the typo so the two solutions agree!

  • calc -

    agree thank you steve

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