I'm having trouble solving this problem:
find the derivative of
( (1/square root x) - (square root x) ) ^ 3.
Any help will be appreciated!
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.
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.
((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)
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.