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#1 2006-05-15 06:45:39

Neela
Guest

calculus

Hi everyone, smile

I'm having trouble solving this problem:

find the derivative of

( (1/square root x) - (square root x) ) ^ 3.


Any help will be appreciated!
Thank you smile

#2 2006-05-15 10:33:47

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: calculus

when learning derivatives the best first step is to convert all radicals to fractional exponents.

1/sqrt s = x^(-1/2),    - (sqrt x)^3 = -  x ^ (3/2) 

Now you multiply the coefficient by the exponant, then decrease the exponant by 1.

-1/2 x ^-(3/2) - 3/2 x^(1/2)

Then if you want you might try getting rid of the negative and fractional exponents though its not really necessary.


A logarithm is just a misspelled algorithm.

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#3 2006-05-15 15:02:22

ganesh
Moderator
Registered: 2005-06-28
Posts: 14,534

Re: calculus

Neela,
Your question is

Now, you just got to apply the formula

and you'd get the required solution!


Character is who you are when no one is looking.

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#4 2006-05-15 15:26:39

Mozartmoses
Member
Registered: 2006-04-26
Posts: 10

Re: calculus

((1/square root x) - (square root x))^3

Let us take y = ((1/square root x) - (square root x))^3

On simplifying, we will get...

         y = x^(-3/2) - 3x^(-1/2) + 3x^(1/2) -x^(3/2)
         

Differentiate with respect to x, we will get.


         dy/dx = (-3/2)x^(-5/2) + (3/2)x^(-3/2) + (3/2)x^(-1/2) - (3/2)x^(1/2)

On simplifying

         dy/dx = 3/2(-x^(-5/2) + x^(-3/2) + x^(-1/2) - x^(1/2))

Let me know, if there is any correction in my steps.

  With regards
    Moses

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#5 2006-05-16 03:52:51

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: calculus

oops! Didn't see those extra parenthesis. x_x


A logarithm is just a misspelled algorithm.

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