Question

How do you find the derivative of `y=ln((2x)/(x+3))`?

Answer 1

You could immediately use: `d/(dx)( ln u) = 1/u (du)/(dx)`

which is also written `d/(dx)( ln g(x)) = 1/g(x) g'(x) = (g'(x))/g(x)`.

That will work, another way is to rewrite before differentiating.

`y=ln((2x)/(x+3)) = ln(2) +ln(x) - ln(x+3)`

So `y' = = 1/(x) - 1/(x+3)`

Is you want to rewrite this as a single fraction, do so.