Is there are difference between these functions

F(x,y) = cot(x)*ln(y^2) and

G(x,y) = 2cot(x)*ln(y).

When I sub in (pi/4, 1-1) I get two different answers, but on wolfram alpha the graphs look the same.

F(x,y) = cot(x)*ln(y^2) and

G(x,y) = 2cot(x)*ln(y).

When I sub in (pi/4, 1-1) I get two different answers, but on wolfram alpha the graphs look the same.

YEs they are th same because $\ln y^2=2\ln y$

you mean (pi/4,-1) right?

The problem is caused by the fact your functions are not well-defined: you need a specify a domain. E.g. if you only consider the positive reals as the domain then they are the same but if you include the negative reals then clearly $ln(y^2) \ne 2ln(y)$ just try $y=-1$ then $ln((-1)^2)=ln(1)=0$ but $2ln(-1)=2i\pi$.

To solve this problem you need to view the log as a multivalued complex function: I suspect wolfram alpha views ln(x) as the principle logarithm in which case the rules of logs don't hold in $\mathbb{C}$ in general.

But as tombayes was pointing out, ln y isn't defined for y < 0 whereas ln(y^2) is (unless of course you're extending to the full complex plane, but the notation x and y is suggestive of real variable calciulus only).

Thanks

Can you help me with this Q:

Find the domain and range of f(x,y)= log(x^2-y)

Also I need help sketching functions of several variables such as: f(x,y) = -sqrt(x^2-y^2)