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Math Help - Differentiate fuction

  1. #1
    Junior Member
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    Differentiate fuction

    Differentiate the following function.


    y ' = ?


    ATTEMPT
    y=x^1/2(5x-2)
    = 5x^(3/2)-2x(1/2)
    = (15/2)x^(1/2)-x^(-1/2)

    Then from this step I am lost. So please help me out! THANKS!
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  2. #2
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    Quote Originally Posted by miss.strw View Post
    Differentiate the following function.


    y ' = ?


    ATTEMPT
    y=x^1/2(5x-2)
    = 5x^(3/2)-2x(1/2)
    = (15/2)x^(1/2)-x^(-1/2)

    Then from this step I am lost. So please help me out! THANKS!
    You have done it correctly. Although it is bad form to write it the way you've written it. You should have:

     y = \sqrt{x} (5x - 2)
     y = x^{\frac{1}{2}} (5x - 2)
     y = 5x^{\frac{3}{2}} - 2x^{\frac{1}{2}}

     \therefore y' = \frac{15}{2} x^{\frac{1}{2}} - x^{\frac{-1}{2}}

    Now, you can make it look a bit prettier from here. Remember that  x^{-a} = \frac{1}{x^{a}} . So we can write:

     y' = \frac{15}{2} x^{\frac{1}{2}} - \frac{1}{x^{\frac{1}{2}}}

    Now write it with square root signs!

     y' = \frac{15}{2} \sqrt{x} - \frac{1}{\sqrt{x}} .

    An easier way to do this might been with the product rule, which states that if  y = f(x) g(x) , then  y' = f'(x) g(x) + f(x) g'(x)
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  3. #3
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    Thank you so much!!!! thank you!!!
    i didn't know it can go more than that!
    n make it look "prettier" lol cool!!! thanks! learnt something!
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