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Math Help - implicit differenitaion

  1. #1
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    implicit differenitaion

    so the problem asks us to solve for \frac{d^2y}{dx^2} from the equation
    x^5+y^5=4

    I found \frac{dy}{dx}=\frac{(-5x^4)}{(5y^4)}, how would I go about solving for \frac{d^2y}{dx^2}?
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  2. #2
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    Quote Originally Posted by ascendancy523 View Post
    so the problem asks us to solve for \frac{d^2y}{dx^2} from the equation
    x^5+y^5=4

    I found \frac{dy}{dx}=\frac{(-5x^4)}{(5y^4)}, how would I go about solving for \frac{d^2y}{dx^2}?
    Cancel 5 to make things easier, then use the quotient rule

    I get
    \frac{4x^3(y-x)}{y^5}
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  3. #3
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    Quote Originally Posted by ascendancy523 View Post
    so the problem asks us to solve for \frac{d^2y}{dx^2} from the equation
    x^5+y^5=4

    I found \frac{dy}{dx}=\frac{(-5x^4)}{(5y^4)}, how would I go about solving for \frac{d^2y}{dx^2}?
    I get ...

    \frac{d^2y}{dx^2} = - \frac{16x^3}{y^9}
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  4. #4
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    Quote Originally Posted by skeeter View Post
    I get ...

    \frac{d^2y}{dx^2} = - \frac{16x^3}{y^9}
    I got a different answer from both of you but I typed in \frac{d^2y}{dx^2} = - \frac{16x^3}{y^9} and it was right. How did you go about solving it?
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