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Ravus

  • 2 years ago

derivative of: sqrt(x) - x using the first principal. Please show work. The answer should be 1/[2*sqrt(x)]-1 I cant get the minus 1!

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  1. experimentX
    • 2 years ago
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    i guess you know how to find the derivate of x ... so just find for sqrt(x)

  2. Ravus
    • 2 years ago
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    f(x) = \[\sqrt{x} -x \]

  3. Ravus
    • 2 years ago
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    oh...so just do them one at a time?:| That actually makes a lot of sense. the problem is I have the equation in the "definition of the derivative formula" and its not simplifying down right.

  4. Ravus
    • 2 years ago
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    where you take the limit as h-->0

  5. experimentX
    • 2 years ago
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    lim dx->0 (sqrt(x+dx) - sqrt(x))/dx now sqrt(x+dx) = sqrt(x)*sqrt(1+dx/x) using binomial expansion, and removing higher terms --- close to linear expression we have: sqrt(x)(1+1/2*dx/x) or, lim dx->0 (sqrt(x)(1+1/2*dx/x) - sqrt(x))/dx or, lim dx->0 (1/2*dx/sqrt(x))/dx = 1/(2sqrt(x)) hence proved

  6. lgbasallote
    • 2 years ago
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    seems he wants the increment thingy...the limits

  7. dpaInc
    • 2 years ago
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    @Ravus , are you asking to take the derivative using the definition? (limit definition of derivative)

  8. perl
    • 2 years ago
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    @experimentX how do you get this sqrt(x+dx) = sqrt(x)*sqrt(1+dx/x)

  9. dpaInc
    • 2 years ago
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    @perl, nice avatar!

  10. perl
    • 2 years ago
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    hehe

  11. Ravus
    • 2 years ago
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    yes I want the "increment thingy"<<<thats exactally it! and yes dpalnc, I think it is the limit definition I mean.

  12. experimentX
    • 2 years ago
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    @perl .. take x common!

  13. perl
    • 2 years ago
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    huh?

  14. dpaInc
    • 2 years ago
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    |dw:1333351654824:dw| plug it in to that...

  15. perl
    • 2 years ago
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    (x+dx)^1/2 = x^1/2 + ...

  16. perl
    • 2 years ago
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    ohhhh

  17. Ravus
    • 2 years ago
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    yeah I did plug it in, and I get the right answer almost. I get 1/2*sqrt(x) but that whole thing should have a "-1"! i dont get that bit

  18. perl
    • 2 years ago
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    @experimentX (x+dx)^1/2 = x^1/2 ( 1 + dx/x ) ^1/2

  19. experimentX
    • 2 years ago
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    dx is supposed to be del x ... or better h

  20. dpaInc
    • 2 years ago
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    |dw:1333351804706:dw| do some algebra here....

  21. dpaInc
    • 2 years ago
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    ok... too many cooks... i'll quit.

  22. Ravus
    • 2 years ago
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    yeah I know what the formula is, but the algebra is giving me trouble

  23. perl
    • 2 years ago
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    @experimentX Very clever argument, so you looked at the binomial series and took the first two terms (linear )

  24. experimentX
    • 2 years ago
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    yes .. since dx^higer would be very less ... it would seem better to take linear term.

  25. perl
    • 2 years ago
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    then you factored out sqrt x

  26. experimentX
    • 2 years ago
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    yes .. and that would cancel out .. sqrt(x) leaving dx/(2sqrt(x)

  27. Ravus
    • 2 years ago
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    omg wow finally got it. simple algebra really. lmfao............

  28. experimentX
    • 2 years ago
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    congrats

  29. gurvinder
    • 2 years ago
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    |dw:1333354174909:dw|

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