Determine the derivative of the function:

Question

Y=1 / (Sq.root of (3x-1)

I know the answer is -3 / (2(Sq.root of 3x-1)^3

I just need some aid on the steps.

Thanks in advance.

Answer 1

What if we wrote it like this ...
y = 1/√(3x-1)
= (3x-1)^(-1/2)

now we can use the chain rule

dy/dx = (-1/2)(3x-1)^(-3/2)(3)
= (-3/2)/(3x-1)^(3/2)
= -3/[2√(3x-1)^3

Answer 2

dy/dx=3/2(3x-1)61/2

Answer 3

dy/dx=3/2(3x-1)^1/2

My bad.... apparently didn't hit the shift key for the ^ sign...