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Math Help - (chain rule) implicit differentition

  1. #1
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    (chain rule) implicit differentition

    using chain rule F(x,y)= y^5+x^2 y^3-ye^x^2-1=0
    thank you again
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    Quote Originally Posted by fearless901 View Post
    using chain rule F(x,y)= y^5+x^2 y^3-ye^x^2-1=0
    thank you again
    Differentiate this function implicitly? but with respect to x or y?
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  3. #3
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    Quote Originally Posted by pickslides View Post
    Differentiate this function implicitly? but with respect to x or y?
    compute using dy/dx using chain rule
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  4. #4
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    Quote Originally Posted by fearless901 View Post
    using chain rule F(x,y)= y^5+x^2 y^3-ye^x^2-1=0
    thank you again
    \frac{dy}{dx}=-\frac{F_x}{F_y}=-\frac{2xy^3-2xye^{x^2}}{5y^4+3x^2y^2-e^{x^2}}
    Last edited by TheEmptySet; April 21st 2009 at 09:01 PM. Reason: missing negative sign
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  5. #5
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    ty theemptyset, but can u tell me how you come about the answer?? thank you so much, i stink at math, but i like it
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  6. #6
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    nvm i got
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  7. #7
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    Quote Originally Posted by fearless901 View Post
    nvm i got
    Really? TheEmptySet actually used a shortcut from multivariable Calculus. He didn't do it by implicit differentiation and then solving for dy/dx. If you would like to, show us how you did the problem so others may use this thread in the future as a reference.
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  8. #8
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    well i just did it seperately
    using:
    dF/dx= 2xy^3-2xye^x^2

    dF/dy= 5y^4+3x^2y^2-e^x^2

    not sure it helped, basically the same thing as TheEmptySet
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  9. #9
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    Quote Originally Posted by fearless901 View Post
    ty theemptyset, but can u tell me how you come about the answer?? thank you so much, i stink at math, but i like it
    Try this link, tis a goodie.

    http://archives.math.utk.edu/visual....licit.7/4.html
    Last edited by pickslides; April 21st 2009 at 09:03 PM. Reason: Typo
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  10. #10
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    Oh ok. You didn't do implicit differentiation. You used partial differentiation. That is fine of course I just assumed by the thread title that you were in a Calc I or II class, not Calc III.
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  11. #11
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    yea im in calc III, sry for the misunderstanding
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  12. #12
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    Quote Originally Posted by pickslides View Post
    Try this link, tis a goodie.

    Visual Calculus - Implicit Differentiation
    Nice website thxs, BOOKMARKED
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  13. #13
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    Quote Originally Posted by Jameson View Post
    Really? TheEmptySet actually used a shortcut from multivariable Calculus. He didn't do it by implicit differentiation and then solving for dy/dx. If you would like to, show us how you did the problem so others may use this thread in the future as a reference.
    eeppp I need to pay more attention. I thought that is what we wanted. I will add this for completeness

    Suppose y=f(x) and that

    F(x,y)=0 then we get

    F(x,y)=0 then by implict differentation and the chain rule we get

    \frac{dF}{dx}\cdot \frac{dx}{dx}+\frac{dF}{dy}\frac{dy}{dx}=0


    F_x+F_y\frac{dy}{dx}=0 \iff F_y\frac{dy}{dx}=-F_x \iff \frac{dy}{dx}=-\frac{F_x}{F_y}
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