How do you determine the derivative of f when?

Question

f(x)= root (6x) – (1 / root (6x))

Answer 1

It's easier to take away those roots by making it a fraction (root x = x^1/n). This way its easier to find the derivative.

(6x)^1/2 - (6x)^-1/2 =

(1/2 * 6x^(1/2) -1) - (-1/2 * 6x^(-1/2) -1) =

3x^-1/2 + 3x^-3/2

Answer 2

Assuming f(x) is:-
f(x) = √6.x^(1/2) - (1/√6).x^(-1/2)
f `(x) = (1/2).√6.x^(-1/2) + (1/√6).(1/2).x^(-3/2)
f `(x) = (1/2).x^(-3/2).[ √6.x + 1/√6 ]

Answer 3

f(x)= (6x)^.5 – (6x)^-.5
f'(x) = .5*6*(6x)^-.5 - .5*6*(6x)^-1.5