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Math Help - Chain rule?

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    58

    Chain rule?

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

    If I want to find the derivative of this, I figured I should use the chain rule on this one:
    \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
    Joined
    Feb 2009
    From
    Scotland
    Posts
    41
    The answer you got is almost right. It should be:
     2y\frac{dy}{dx}
    I'm going to name this equation as follows
     f = y^2
    I'm using f instead of the traditional y so the equation makes sense

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

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

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

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