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Partial derivative

  1. Jul 16, 2006 #1
    f(x,y)=2y / (y+cos x) .Find partial derivative w.r.t x

    can someone teach me how to do this pls

  2. jcsd
  3. Jul 16, 2006 #2


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    If y doesn't depend on x, treat y as a constant and find the derivative wrt x as you normally do.
  4. Jul 16, 2006 #3


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    Staff: Mentor

    To do a partial derivative with respect to one variable, treat the other variables as 'constants'. In the equation given, for a partial derivative with respect to x, treat y as a constant and use the rules for ordinary differentiation.
  5. Jul 16, 2006 #4


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    Since you're doing multiple-variable calculus, you probably know how to differentiate the function f(x) = 2k / (k+cos x ) where k is a constant? Find that, then replace k by y and you get the partial derivative of f(x,y) wrt x.
  6. Jul 16, 2006 #5
    can someone show this because i don't know how to do
  7. Jul 16, 2006 #6
    Just Differentiate f(x) as if y was a constant. Just concentrate on the x variable, the only one that is "important" now. The derivative of the function f(x) = 2k/(k+cos x ) where k is a constant (and then changing k for y) is the same as the partial derivative of f(x,y)=2y / (y+cos x) w.r.t x.
    Nothing else is to be shown.
  8. Jul 16, 2006 #7
    the formula is it vu'-u'v/(v^2) ??
  9. Jul 16, 2006 #8


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    Uhmm, nope. The red-highlighted part is wrong. It should read uv', i.e the whole formula is:
    [tex]\left( \frac{u}{v} \right) ' = \frac{u'v - uv'}{v ^ 2}[/tex].
    Can you go from here? :)
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