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Math Help - find dirivitive of T(t)

  1. #1
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    find dirivitive of T(t)

    let  \vec T(t) = \frac{1}{\sqrt{10+ 4t^2}} ( 3 \hat i - \hat j + 2t \hat k) find \frac {d \vec T}{dt}


    I am not sure how to do this.
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  2. #2
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    Re: find dirivitive of T(t)

    Note that

    \frac{d}{dt} \frac{1}{\sqrt{10 + 4t^2}} = -4t (10+4t^2)^{-\frac{3}{2}}, and

    \frac{d}{dt} \frac{2t}{\sqrt{10 + 4t^2}} = \frac{2 \sqrt{10 + 4t^2} - t(10 + 4t^2)^{-\frac{1}{2}}}{10 + 4t^2} (applying the chain and quotient rules)

    \frac{d \vec{T}}{dt} is computed by taking the derivatives of each of vector T's components, i.e.

    \frac{d \vec{T}}{dt} = \frac{d}{dt} \frac{3}{\sqrt{10 + 4t^2}}\vec{i} - \frac{d}{dt} \frac{1}{\sqrt{10 + 4t^2}} \vec{j} + \frac{d}{dt} \frac{2t}{\sqrt{10 + 4t^2}} \vec{j}

    Use the given derivatives and substitute.
    Thanks from icelated
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