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Math Help - derivative q's

  1. #1
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    derivative q's

    Find the derivative. State the domain of the function and the domain of its derivative.

    f(x) = x + √x

    f(x) = (3 + x) / 1-3x

    Find F'(a)

    f(x) = (x^2 + 1) / (x - 2)

    f(x) = √3x + 1
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  2. #2
    MHF Contributor Reckoner's Avatar
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    Quote Originally Posted by bballj228 View Post
    Find the derivative. State the domain of the function and the domain of its derivative.

    f(x) = x + √x

    f(x) = (3 + x) / 1-3x

    Find F'(a)

    f(x) = (x^2 + 1) / (x - 2)

    f(x) = √3x + 1
    What's giving you trouble?

    For the first, rewrite: x + \sqrt x = x + x^{1/2} and use the power rule. The second can be done simply with the quotient rule.

    The third can also be done with the quotient rule, but it would be easier to reduce the fraction (factor the numerator).

    For the fourth, use the chain rule:

    \frac d{dx}\left[\sqrt{3x} + 1\right] = \frac d{dx}\left[(3x)^{1/2} + 1\right] = \frac12(3x)^{-1/2}\frac d{dx}\left[3x\right]
    Last edited by Reckoner; June 24th 2008 at 09:08 AM. Reason: Error correction
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  3. #3
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    Almost right

    x^(1/2)+x^1=x^(1/2)*(1+x^(1/2)) not x^(3/2). Differentiate each term with the power rule, the factorization makes it more complicated.
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Reckoner View Post
    For the first, rewrite: x + \sqrt x = x + x^{1/2} = x^{3/2}
    Last time I checked

    x^a+x^b\ne{x^{a+b}}
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  5. #5
    MHF Contributor Reckoner's Avatar
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    Quote Originally Posted by Mathstud28 View Post
    Last time I checked

    x^a+x^b\ne{x^{a+b}}
    Ha ha! That's a pretty bad mistake. Maybe I was too tired to notice the addition symbol in there.
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