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Thread: Chain rule?

  1. #1
    Junior Member
    Mar 2008

    Chain rule?

    Ok, so in an equation I have the following:
    $\displaystyle y^2$

    If I want to find the derivative of this, I figured I should use the chain rule on this one:
    $\displaystyle \frac{dy}{dy} \cdot \frac{dy}{dx}=1 \frac{dy}{dx}$

    But is that correct? I don't get it if it's wrong. :/
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  2. #2
    Junior Member
    Feb 2009
    The answer you got is almost right. It should be:
    $\displaystyle 2y\frac{dy}{dx} $
    I'm going to name this equation as follows
    $\displaystyle f = y^2 $
    I'm using f instead of the traditional y so the equation makes sense

    The chain rule states $\displaystyle \frac{dy}{dx} = \frac{dy}{du} * \frac{du}{dx} $

    In your case where $\displaystyle u = y $
    $\displaystyle f = u^2 $
    $\displaystyle \frac{df}{du} = 2u $

    Then when:
    $\displaystyle u = y $
    $\displaystyle \frac{du}{dx} = \frac{dy}{dx} $

    So using the chain rule in this case you get:
    $\displaystyle \frac{df}{dx} = \frac{df}{du} * \frac {du}{dx} $
    $\displaystyle \frac{df}{dx} = 2u * \frac{dy}{dx} $
    Substituting y back in it becomes:
    $\displaystyle 2y\frac{dy}{dx} $

    You had the right idea and almost got it correct. The chain rule can be easy to mess up especially when y is involved.
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