calculus
posted by mike on .
find the derivative of the function (6x+1)/(19x+1)^1/2
PLEASE EXPLAIN IM LOST

You use the quotient rule of :[u'v uv']/v^2
so:
u=(6x+1) v=(19x+1)^1/2
u'=6 v'= [1/2(19x+1)^1/2] (19)
y' = 6[(19x+1)^1/2]  (6x+1)[1/2(19x+1)^1/2] (19)
you can simplify it by taking a common factor. In this case its easier to take (19x+1)^1/2 Always take the lowest common factor.
y'=[[19x+1]^1/2] 6(19x+1) (6x+1)(1/2)(19)
y'=[[19x+1]^1/2] 114x+657x+9.5
Final answer:
y'=[[19x+1]^1/2] 57x + 15.5