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Math Help - The Derivative as a unction

  1. #1
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    The Derivative as a unction

    If f(t)= √((t^2-1)/(t^2-1))
    Find f '(t)
    I have tried it several times using f(x+h)-f(x) / h, but I always get lost and don't know how to solve it.
    Could someone help me?
    Thank you
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  2. #2
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    Quote Originally Posted by Raimuna View Post
    If f(t)= √((t^2-1)/(t^2-1))
    Find f '(t)
    I have tried it several times using f(x+h)-f(x) / h, but I always get lost and don't know how to solve it.
    Could someone help me?
    Thank you
    are you sure it is  f(t)=\sqrt {\frac{t^2-1}{t^2-1} } ?
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  3. #3
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    Quote Originally Posted by Raimuna View Post
    If f(t)= √((t^2-1)/(t^2-1))
    Find f '(t)
    I have tried it several times using f(x+h)-f(x) / h, but I always get lost and don't know how to solve it.
    Could someone help me?
    Thank you
    That's the function?

    f(t)=\sqrt{\frac{t^2-1}{t^2-1}}=1

    ??

    It's probably this:

    f(t)=\frac{\sqrt{t^2-1}}{t^2-1}

    right?
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  4. #4
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    Quote Originally Posted by ramiee2010 View Post
    are you sure it is  f(t)=\sqrt {\frac{t^2-1}{t^2-1} } ?
    sory, my bad. the denominator should be t^2+1
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  5. #5
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    So we want to evaluate the limit:

    \lim_{h->0}(\frac{\sqrt{(t+h)^2-1}}{h(t+h)^2-h}-\frac{\sqrt{t^2-1}}{ht^2-h})
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  6. #6
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    Why dont you just use the rules of differntiation?
    I dont see why you would try to find the derivative of f using the limit definition of the derivative.

    Two obvious approaches that stand out.

    first you could use the chain rule followed by the quotient rule for differentiation.

    or simplify

    f(t)=\sqrt {\frac{t^2-1}{t^2 + 1} } =  \frac{\sqrt {t^2-1}} {\sqrt{t^2 + 1}}

    then use the quotient rule and chain rule.

    I find after some quick and sloppy calculations (so forgive me if this is not completely accurate)

    f'(t) = \frac{2t}{(t^2 - 1)(t^2 + 1)^{3/2}}
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