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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
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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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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((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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oops! Didn't see those extra parenthesis. x_x
A logarithm is just a misspelled algorithm.
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