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Math Help - Derivative help

  1. #1
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    Derivative help

    Have to find derivatives of following problems:




    For this one, I simplified to :

    (-4x^5 * x^(1/2)) + ((-7)/(x^3 * x^1/2))

    -4^(11/2) + -7x^(-7/2)

    Ended with:

    -22x^(9/2) + (-49/2*x^(-9/2))

    Is there something I'm doing wrong?




    For this one I tried making it :

    5^(1/2) * t^-3

    -15^-3/2 * t^-4

    ended with 1/(15^(3/2) * t^4)

    Is that correct?



    I ended with 4/(x^(1/2))

    Correct?



    For this one, how would I do about solving this with the x on the bottom also?



    Lastly:


    How do you find the derivative at that point?

    I got -6x-3 for the line, but what do i do after that?
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  2. #2
    Super Member TheChaz's Avatar
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    Re: Derivative help

    For the first one, I think the second term should be positive (-7 * -7/2 = 49/2).
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  3. #3
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    Re: Derivative help

    \frac{\sqrt{5}}{t^3} = \sqrt{5} \cdot t^{-3}

    \frac{d}{dt} \left[\sqrt{5} \cdot t^{-3}\right] =

    \sqrt{5} \frac{d}{dt} \left[t^{-3}\right] =

    \sqrt{5} \left(-3t^{-4})

    -\frac{3\sqrt{5}}{t^4}

    in future, don't bump
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  4. #4
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    Re: Derivative help

    Quote Originally Posted by FrustratedCollegeKid View Post
    Have to find derivatives of following problems:




    For this one, I simplified to :

    (-4x^5 * x^(1/2)) + ((-7)/(x^3 * x^1/2))

    -4^(11/2) + -7x^(-7/2)

    Ended with:

    -22x^(9/2) + (-49/2*x^(-9/2))

    Is there something I'm doing wrong?

    The first term is correct, but the second term is not.

    \frac d {dx} (-7x^{-\frac 7 2}) = (-7) \frac d {dx} x^{-\frac 7 2}=-7 [(-\frac 7 2)x^{-\frac 7 2 - 1}] = \frac {49} 2 x^{-\frac 9 2}
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  5. #5
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    Re: Derivative help

    Quote Originally Posted by FrustratedCollegeKid View Post


    For this one I tried making it :

    5^(1/2) * t^-3

    -15^-3/2 * t^-4

    ended with 1/(15^(3/2) * t^4)

    Is that correct?
    It's hard to read your results, but I do not think it is correct.
    \frac d {dx} \sqrt{5} t^{-3} = \sqrt{5} \frac d {dx} t^{-3} = \sqrt{5} [(-3)t^{-3 -1}] = -3\sqrt 5 t^{-4}
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  6. #6
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    Re: Derivative help

    Quote Originally Posted by FrustratedCollegeKid View Post


    I ended with 4/(x^(1/2))

    Correct?
    No, this one is wrong. If you've learned the chain rule, it is helpful to just memorize the derivative of the square root as a separate rule, since it comes up so often. That is,

    \frac d {dx} \sqrt{f(x)} = \frac {f'(x)} {2\sqrt{f(x)}}

    If you haven't learned the chain rule yet, then do this as the power rule:

    \frac d {dx} \sqrt{8x} = \sqrt 8 \frac d {dx}x^{\frac 1 2} = \sqrt 8 [(\tfrac 1 2)x^{\frac 1 2 - 1}] = 2\sqrt 2 [\tfrac 1 2 x^{-\frac 1 2}] = \sqrt{\frac 2 x}
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  7. #7
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    Re: Derivative help

    Quote Originally Posted by FrustratedCollegeKid View Post


    For this one, how would I do about solving this with the x on the bottom also?
    You need to use the quotient rule. Refer to your textbook, or this site:
    Quotient Rule for Derivatives - HMC Calculus Tutorial
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  8. #8
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    Re: Derivative help

    Quote Originally Posted by FrustratedCollegeKid View Post


    How do you find the derivative at that point?

    I got -6x-3 for the line, but what do i do after that?
    Your formula for the derivative is correct. Now, you are given a pair of values in (x,y) form. If you plug 5 into f(x), you'll see that you get -79 "out", or more formally we have that f(5)=-79. This is a point on the curve given by that equation. Now they want to know what the value of the derivative is at this point, that is, the point where x=5. So, you have f'(x)=-6x-3, and you want to know what f'(5) is...
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