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Simple calculus question

  1. Oct 17, 2006 #1
    Hi,

    could someone please clarrify how to do this step? It's midway through a large problem and I'm not so sure about it.

    y is a function of x.

    [tex]\frac {d}{dx} ( \frac {y} \sqrt{1 + y'}} )[/tex]

    Please excuse the Latex. The square root of 1 + y' is being taken on the denominator .

    Do you just use the quotient rule? and does [itex] \frac {d} {dx}y[/itex] equal [itex]y'[/itex]?

    thanks
     
    Last edited: Oct 17, 2006
  2. jcsd
  3. Oct 17, 2006 #2
    I can't see the LaTeX but dy/dx does equal y'.

    dy/dx is Leibniz's notation and using the prime mark is Lagrange's notation.

    f(x)=y, so f'(x)=y' and if y is a function of x then the dy/dx means the derivative of y with respect to x.
     
    Last edited: Oct 17, 2006
  4. Oct 17, 2006 #3
    Yes, use the quotient rule. To differentiate the square root expression you could use the chain rule. It may help to look at the denominator as [tex](1+y')^\frac{1}{2}[/tex].
     
  5. Oct 17, 2006 #4

    HallsofIvy

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    Science Advisor

    Further, since that is a function of y and you are differentiating with respect to x, you will have to multiply each derivative by y'.
     
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