Question

Differentiate:
y=ln(x/(2x+3))^(1/2)
y=(1/2)ln(x/(2x+3))
y'=0+(1/2)((2x+3-2x)/(2x+3)²)

What's next after the quotient rule?

Answer 1

You don't have to use the quotient rule of differentiation.

y = lnx - (1/2)ln(2x+3)
y' = 1/x -(1/2)[1/(2x+3)]*2
= (1/x) - [1/(2x+3)]
which can be rewitten with a common denominator, if you wish.

Answer 2

Thanks for your help!