Results 1 to 2 of 2

Math Help - Help w/ implicit differentiation

  1. #1
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432

    Help w/ implicit differentiation

    I don't really get this method, it wasn't explained thoroughly in the book. It says:
    "Differentiate term by term through the function, remembering that in differentiating functions of y you are differentiating a function of a function".

    Then it gives an example:

    Find \frac{dy}{dx} of x^2-y^2 +3x = 5y
    2x-2y\frac{dy}{dx}+3=5\frac{dy}{dx}
    \frac{dy}{dx}=\frac{2x+3}{2y+5}

    I don't know why \frac{d}{dx}(y^2)=2y\frac{dy}{dx}. I know that y is really a polynomial in x and that 'somehow' complicates things, but it doesn't make sense to me to just add a \frac{dy}{dx} to the end
    I also never knew you could differentiate an 'equation'... could you effectively write this \frac{d}{dx}(Equation )?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    When you have \frac{dy}{dx} you know you're differentiating respect to x, and when you take the derivative of y, you use the chain rule, for that reason yields \frac{dy}{dx}~y^2=2yy'
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 26th 2010, 06:24 PM
  2. implicit differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 1st 2010, 08:42 AM
  3. Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 28th 2010, 04:19 PM
  4. Implicit differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 26th 2010, 06:41 PM
  5. Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 25th 2008, 08:33 PM

Search Tags


/mathhelpforum @mathhelpforum