Help with differentiation?

Question

Can anyone help me differentiate these? Really confused, thanks!

a) (3x+2)/ root x
b) ((2 root x) - 1) / x

Answer 1

a) (3x + 2)/√x

= (3x + 2)(x^-1/2)

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

Differentiating with respect to x.

= 3[ (1/2)x^1/2-1] + 2 [ (-1/2)x^-1/2-1]

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

Derivative of (3x + 2)/√x is  3/(2√x) - 1/(√x)³.

Answer 2

b) (2√x - 1)/x

Differentiating with respect to x.

Apply quotient rule in derivatives d/dx(u/v) = [vu' - uv']/v²

u = 2√x - 1, v = x

u' = 1/√x , v' = 1

d/dx[(2√x - 1)/x] = [ x(1/√x) - (2√x - 1)(1)]/x²

= (√x - 2√x + 1)x²

Derivative of (2√x - 1)/x =  (- √x + 1)/x²