Question

Is the derivative of (squarerootof x)/(3x+1) : 3x+1-3squarerootofx/(2squarerootofx)(3x+1)^2

Answer 1

y = √x/(3x+1)

y' = (1/2√x (3x+1) - √x (3)) / (3x+1)^2
= (3x+1) - 2√x√x(3)) / 2√x (3x+1)^2
= (1-3x) / 2√x (3x+1)^2

Looks like you forgot a factor of √x:

y = u/v
y' = (u'v - <b>u</b>v')/v^2

Answer 2

also ,my own typing was sloppy.

y' = (1/(2√x) (3x+1) - √x (3)) / (3x+1)^2

Looks like you forgot to put the numerator over a common denominator of 2√x