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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

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: calculus

Neela,
Your question is

Now, you just got to apply the formula

and you'd get the required solution!


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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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