I am trying but it is really hard learning this stuff on your own. Never gonna take a calc course online again :\.
This it he question, I am currently stuck on.
Where is the function analytic?
For now could someone just help me with the derivative? I am in the process of figuring out Couchy-Rieman equations.
Is the derivative only present if u/ x = v/ y?
just for my understanding in the equation there is no derivative because u/ x = 0 and v/ y = 1?
Thanks for the quick response. I understand that you have taken the derivatives and in this example the Cauchy-Riemann equations are satisfied.
I am unsure what this means though and where to go from here? No need to carry out the math (although it is helpful), however if possible a short explanation ?
how would I express the final derivative? , is it just the range of equations?
You asked where the function is analytic. The first step is to check where the partial derivatived exist and satisfy the Cauchy-Riemann equations, and as you can see they are satisfied everywhere. If the function is also continuous in that domain, then the function is analytic there (Looman-Menchoff's theorem).
The derivative at that point can be written as