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Math Help - Derivative of y^2 = ax

  1. #1
    Member Furyan's Avatar
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    Derivative of y^2 = ax

    Hello

    If I want to find the gradient at any point on a parabola with an equation of the form:

    y^2 = ax , where  a > 0

    Do I use \dfrac{dy}{dx} = \dfrac{a}{2\sqrt{ax}}

    knowing that when  y > 0, \dfrac {dy}{dx} > 0 and that when  y < 0, \dfrac {dy}{dx} < 0 or is there another way? I noticed when I used implicit differentiation I didn't get an x term in the derivative.

    Thank you
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  2. #2
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    skeeter's Avatar
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    Re: Derivative of y^2 = ax

    implicit is the way to go ...

    2y \cdot \frac{dy}{dx} = a

    \frac{dy}{dx} = \frac{a}{2y}
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  3. #3
    Member Furyan's Avatar
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    Re: Derivative of y^2 = ax

    Thank you skeeter

    Quote Originally Posted by skeeter View Post
    implicit is the way to go ...

    2y \cdot \frac{dy}{dx} = a

    \frac{dy}{dx} = \frac{a}{2y}
    I replaced my 2y with  2\cdot\dfrac{dy}{dx} instead of 2y \cdot \frac{dy}{dx}, so I didn't have a y term in the derivative either. That's why I was confused.

    Thank you very much and a very happy New Year to you.
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