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**Neela****Guest**

Hi everyone,

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

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

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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,983

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

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

oops! Didn't see those extra parenthesis. x_x

A logarithm is just a misspelled algorithm.

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