Question

differentiation of a quotient with respect to x of y=(ln 2 x)/sqrt x

Answer 1

Apply the quotient rule.\[\frac {d}{dx} \left[ \frac {u}{v} \right] = \frac {vu' - uv'}{v^2}\]

Answer 2

i think i have done that want to check my answer - i get dy/dx = x^-3/2(1+ln2x/2x) does this seem sensible

Answer 3

It should be x^(-3/2)(1 - ln(2x)/2).
You might've made a factoring error.

Answer 4

okay - feel i on the right lines - thank you