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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: 19,197

Re: calculus

Neela,
Your question is

Now, you just got to apply the formula

and you'd get the required solution!


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

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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