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Math Help - Derivatives

  1. #1
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    Derivatives

    1-t^2/3+t^4
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  2. #2
    Junior Member Bradyns's Avatar
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    Re: Derivatives

    The way that you've written this question is slightly ambiguous... You should use brackets.

    Polynomial terms.
    \frac{\mathrm{d} }{\mathrm{d} x} x^{n} = nx^{n-1}

    Constants.
    \frac{\mathrm{d} }{\mathrm{d} x} k = 0

    Case#1
    \frac{\mathrm{d} }{\mathrm{d} t} -t^{\frac{2}{3}}+\frac{\mathrm{d} }{\mathrm{d} t}t^4 + \frac{\mathrm{d} }{\mathrm{d} t}1 = -\frac{2}{3t^{\frac{1}{3}}} + 4t^{3}

    Case#2
    \frac{\mathrm{d} }{\mathrm{d} t} \frac{-t^{2}}{3}+\frac{\mathrm{d} }{\mathrm{d} t}t^4 + \frac{\mathrm{d} }{\mathrm{d} t}1 = -\frac{2t}{3} + 4t^{3}

    Again, please use brackets to avoid ambiguity. :/
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  3. #3
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    Re: Derivatives

    Or even \displaystyle \begin{align*} \frac{d}{dt} \left( \frac{ 1 - t^2 }{ 3 + t^4 } \right) &= \frac{ -2t \left( 3 + t^4 \right) - 4t^3 \left( 1 - t^2 \right) }{ \left( 3 + t^4 \right) ^2} \end{align*}

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