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Math Help - Differentiating

  1. #1
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    Differentiating

    Hey guys the question asks to prove d/dt (Sin^-1(e^t)) = (e^-2t-1)^-1/2

    I've got that the derivative is e^T/(1-e^2t)^1/2 but how do I get that to be the right hand side of the equation?
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  2. #2
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    Quote Originally Posted by Mathsnewbie View Post
    Hey guys the question asks to prove d/dt (Sin^-1(e^t)) = (e^-2t-1)^-1/2

    I've got that the derivative is e^T/(1-e^2t)^1/2 but how do I get that to be the right hand side of the equation?
    Multiply your last expression by \frac{\displaystyle\frac{1}{\sqrt{e^{2t}}}}{\displ  aystyle\frac{1}{\sqrt{e^{2t}}}}
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  3. #3
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    Can you explain to me how that works out? I multiply both the top and bottom by that but still don't get any furhter
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  4. #4
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    Quote Originally Posted by Mathsnewbie View Post
    Can you explain to me how that works out? I multiply both the top and bottom by that but still don't get any furhter
    Use the chain rule on the left hand side to differentiate and get \frac{e^t}{\sqrt{1 - e^{2t}}}.

    Now use Chop'S hint to show that the the right hand side is equal to this expression.
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  5. #5
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    I think I must be multiplying it out wrong, I get when I multiply it out

    ((E^2t)^1/2).E^t/

    (E^2t-(E^2t)^2)^1/2

    From there I can't figure out a way to simplify further.
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