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Thread: Finding the derivative sans quotient rule

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    Question Finding the derivative sans quotient rule

    Find the derivative of the following equation;

    (hint: do not use the quotient rule)

    x^2 - 4
    -------
    x^4


    Is the hint a trick? I'm not sure whether this equation is even differentiable, when graphed it isn't continuous and to be differentiable an equation has to be continuous, right?
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    Quote Originally Posted by rdryden View Post
    Find the derivative of the following equation;

    (hint: do not use the quotient rule)

    x^2 - 4
    -------
    x^4


    Is the hint a trick? I'm not sure whether this equation is even differentiable, when graphed it isn't continuous and to be differentiable an equation has to be continuous, right?
    It's obviously not differentiable at x = 0 since the function is not continuous at x = 0.


    Divide everything by x^4.


    So \frac{x^2 - 4}{x^4} = x^{-2} - 4x^{-4}.


    Can you find the derivative now?
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