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Math Help - n Order Derivative Quotient Problem

  1. #1
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    n Order Derivative Quotient Problem

    f^{(n)}(a), g^{(n)}(a), their nth ord. derivatives exist and are not zero then \Big(\frac{f}{g}\Big)^{(n)} = \frac{g(a)f^{(n)}(a) + (-1)^nf(a)g^{(n)}(a)}{g^{(n+1)}(a)}. So, how should I start off? Should I let h(x):= \frac{1}{g} then we have \Big(\frac{f}{g}\Big)^{(n)} = (f(x)\cdot h(x))^{(n)} Or is there a better way to approach it? Note: this problem could be false.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Endowed View Post
    f^{(n)}(a), g^{(n)}(a), their nth ord. derivatives exist and are not zero then \Big(\frac{f}{g}\Big)^{(n)} = \frac{g(a)f^{(n)}(a) + (-1)^nf(a)g^{(n)}(a)}{g^{(n+1)}(a)}. So, how should I start off? Should I let h(x):= \frac{1}{g} then we have \Big(\frac{f}{g}\Big)^{(n)} = (f(x)\cdot h(x))^{(n)} Or is there a better way to approach it? Note: this problem could be false.
    Check to see if it's true, but try induction.
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