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!
Character is who you are when no one is looking.
((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.