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    derivative

    what is the second derivative of x^2 + y^2 = s^2

    thanks
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  2. #2
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    Quote Originally Posted by doctorgk View Post
    what is the second derivative of x^2 + y^2 = s^2

    thanks
    Ummm... You are looking for \frac{d^2y}{dx^2}? And I presume s is a constant?

    2x + 2y \frac{dy}{dx} = 0

    \frac{dy}{dx} = -\frac{x}{y}

    \frac{d^2y}{dx^2} = -\frac{y - x \frac{dy}{dx}}{y^2}

    Insert the equation for \frac{dy}{dx}:
    \frac{d^2y}{dx^2} = -\frac{y - x \cdot  -\frac{x}{y}}{y^2}

    \frac{d^2y}{dx^2} = -\frac{y^2 + x^2}{y^3}

    Inserting the original equation:
    \frac{d^2y}{dx^2} = -\frac{s^2}{y^3}

    I'd probably leave it like that.

    -Dan
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