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    ankara55t's Avatar
    ankara55t Posts: 53, Reputation: 2
    Junior Member
    		  
    #1

    Aug 24, 2009, 01:56 PM
    derivative-product rule
    The question is to find the derivative of y = x times the square root of (3x^2 + 1)

    I rewrite this as y = x(3x^2 + 1)^1/2

    Then I find y' = x (1/2)(3x^2 + 1)^-1/2 (6x) + 1(3x^2 + 1)1/2

    Is this right and is there any way to further simply this?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
    		  
    #2

    Aug 24, 2009, 03:42 PM
    Yes, you can. That is where algebra comes in.

    You have , which is correct and well done.

    You can leave it like this or get a common denominator, like so:

    Multiply top and bottom of the right side by




    Now, the denominators are the same. As when adding any fraction.
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