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Math Help - derivative problem

  1. #1
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    derivative problem

    If f(x)= (the fifth root of x^2) - (8/x) then f`(x) = ?

    I started by setting it up as follows
    {x^(2/5)} - (8x^-1)
    I then used the power rule to get:
    {(2/5x)^(-3/5)}-(8x^-2) but that doesn't go through as correct. Can someone point out where I am going wrong?

    Thanks
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  2. #2
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    Quote Originally Posted by juventinoalex View Post
    If f(x)= (the fifth root of x^2) - (8/x) then f`(x) = ?

    I started by setting it up as follows
    {x^(2/5)} - (8x^-1)
    I then used the power rule to get:
    {(2/5x)^(-3/5)}-(8x^-2) but that doesn't go through as correct. Can someone point out where I am going wrong?

    Thanks
    watch your signs ...

    {(2/5x)^(-3/5)}+(8x^-2)
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  3. #3
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    OK, well actually I made a mistake here that I didn't there. I actually entered (2/5x)^(-3/5)+(8/x^-2) but that was wrong. Any other ideas. :-)
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  4. #4
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    Quote Originally Posted by juventinoalex View Post
    OK, well actually I made a mistake here that I didn't there. I actually entered (2/5x)^(-3/5)+(8/x^-2) but that was wrong. Any other ideas. :-)
    \displaystyle \frac{d}{dx}\left(\sqrt[5]{x^2} - \frac{8}{x}\right) = \frac{2}{5}x^{-\frac{3}{5}} + 8x^{-2} = \frac{2}{5\sqrt[5]{x^3}} + \frac{8}{x^2}
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  5. #5
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    Also you are using the power rule incorrectly. The derivative of x^{2/5} is (2/5)x^{-3/5}, not (2/5x)^{-3/5}.
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