Results 1 to 9 of 9

Math Help - Mixed differentiation?

  1. #1
    Banned
    Joined
    May 2011
    Posts
    52

    Mixed differentiation?

    y^2 = cosh(xy) + log(x^2 + y^2).

    Find \frac{dy}{dx}.

    This one has got me well knobbed. I don't even know where to start. Maybe root the whole thing? Can someone give me a pointer please?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by TeaWithoutMussolini View Post
    y^2 = cosh(xy) + log(x^2 + y^2).

    Find \frac{dy}{dx}.

    This one has got me well knobbed. I don't even know where to start. Maybe root the whole thing? Can someone give me a pointer please?
    Use implicit differentiation and the chain rule.

    2y\cdot \frac{d}{dx}y=\sinh(xy)\cdot \frac{d}{dx}(xy)+\frac{1}{x^2+y^2}\cdot \frac{d}{dx}\left(x^2+y^2 \right)

    Can you finish from here
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    May 2011
    Posts
    52
    Thanks, I think I can handle the operations but I don't know what kind of form I would be expected to leave it in? I mean is that not done? Just divide by 2y?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by TeaWithoutMussolini View Post
    Thanks, I think I can handle the operations but I don't know what kind of form I would be expected to leave it in? I mean is that not done? Just divide by 2y?
    No All I did was use the chain rule you need to expand all of these \frac{d}{dx}(xy) and \frac{d}{dx}(x^2+y^2) and then collect all of the y''s

    This is just the 1st step.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Banned
    Joined
    May 2011
    Posts
    52
    Can y be treated as a constant? I'm confused? Would the next step to do the same thing again on the 'new' parts?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by TeaWithoutMussolini View Post
    Can y be treated as a constant? I'm confused? Would the next step to do the same thing again on the 'new' parts?
    y is not a constant y is a function of x. y=f(x) Maybe this will help consider

    \frac{d}{dx}y^2=\frac{d}{dx}[f(x)]^2=\underbrace{2f(x)f'(x)}_{\text{ Chain Rule }}=2yy' this is the idea of implicit differentiation!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Banned
    Joined
    May 2011
    Posts
    52
    So is the \frac{d}{dx}(xy) becomes x\frac{dy}{dx} + y?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by TeaWithoutMussolini View Post
    So is the \frac{d}{dx}(xy) becomes x\frac{dy}{dx} + y?
    yes!
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Banned
    Joined
    May 2011
    Posts
    52
    I did that but then I get an answer with loads of y's and dy/dx's and I don't know how to clean it up...?

    EDIT: Ok, I re-did it and got this horrendously disgusting answer? I don't think its right at all? :S

    \frac{dy}{dx}=\frac{ysinh(xy) + \frac{2x}{x^2+y^2}}{2y-xsinh(xy)-\frac{2y}{x^2+y^2}}
    Last edited by TeaWithoutMussolini; June 9th 2011 at 09:04 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mixed Probability
    Posted in the Statistics Forum
    Replies: 6
    Last Post: October 11th 2010, 02:25 PM
  2. Mixed Problems
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: May 24th 2010, 10:48 AM
  3. Differentiation mixed with Line Equation
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 30th 2009, 08:27 PM
  4. Mixed problems
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 12th 2008, 04:41 PM
  5. Mixed Bag
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 25th 2008, 08:57 PM

Search Tags


/mathhelpforum @mathhelpforum