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Math Help - Derivative

  1. #1
    Junior Member Hardwork's Avatar
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    Derivative

    What's the derivative of \displaystyle {3x^2\frac{d^2y}{dx^2} with respect to x? I don't know what to make of the \dfrac{d^2y}{dx^2}. Can I say \frac{d}{dx}(\frac{d^2y}{dx^2}) = \frac{d^3y}{dx^3}?
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  2. #2
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    You will need to use the product rule. And yes, \frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) = \frac{d^3y}{dx^3}.
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  3. #3
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    Quote Originally Posted by Prove It View Post
    You will need to use the product rule.
    I can do that, thanks.

    And yes, \frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) = \frac{d^3y}{dx^3}.
    Can I ask, why is that?
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  4. #4
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    The derivative of the second derivative is the third derivative.
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  5. #5
    Junior Member Hardwork's Avatar
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    Quote Originally Posted by Prove It View Post
    The derivative of the second derivative is the third derivative.
    I have no idea as to why I didn't think of it that way.
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