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X = (cos@)/(sin@)

  1. Aug 16, 2009 #1
    How do u tak the derivative of

    X = (cos@)/(sin@)
    dx/d@ = ????
     
  2. jcsd
  3. Aug 16, 2009 #2

    statdad

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    Re: Derivative

    Two suggestions:

    first: regardless of the variable name, what function does cosine over sine reduce to?

    second: use ordinary derivative tools for trig functions
     
  4. Aug 16, 2009 #3
    Re: Derivative

    must I merely memorize the derivate of cotangent?
     
  5. Aug 16, 2009 #4

    statdad

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    Re: Derivative

    Well, you should know how to use ALL of the derivative methods you encounter, so you don't have to re-derive them each time you need them. On the plus side: if you take enough math courses learning them will be natural. Good luck in your studies................
     
  6. Aug 16, 2009 #5
    Re: Derivative

    Use the product rule or the quotient rule.
     
  7. Aug 16, 2009 #6
    Re: Derivative

    Isn't derivative of cotangent equal to csc squared???
     
  8. Aug 16, 2009 #7

    jgens

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    Re: Derivative

    Why don't you try deriving it to check ;-)
     
  9. Aug 16, 2009 #8
    Re: Derivative

    Where do i start to derive it?
     
  10. Aug 16, 2009 #9

    jgens

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    Gold Member

    Re: Derivative

    Alright, I'll start you off . . .

    [tex]cot(x) = \frac{cos(x)}{sin(x)}[/itex]

    [tex]\frac{d(cot(x))}{dx} = \frac{d}{dx} \left (\frac{cos(x)}{sin(x)} \right )[/tex]

    Now, can you remember the rule for differentiating the quotient of two functions?
     
  11. Aug 17, 2009 #10
    Re: Derivative

    Try checking using the quotient rule:

    [tex]\left({f \over g}\right)' = {f'g - fg' \over g^2}, \qquad g \ne 0[/tex]

    In your case f=cos@ and g=sin@

    Regards.
     
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