Partial derivative with unknown function f(x,y)

Question

I got a task from my lecture, i have tried to do that and this is my solution for the task. I was confused because the function f(x,y), g(r,$\theta$), and h(r,$\theta$) were not defined, so i just can use the value of that functions.

[Click on this link to see my solution] (https://i.stack.imgur.com/MpxJN.png)

Is it my solution correct? Thanks for any help.

Answer 1

$$ \frac{\partial f}{\partial r} = \frac{\partial f}{\partial x} \frac{\partial x}{\partial r} + \frac{\partial f}{\partial y} \frac{\partial y}{\partial r} = 2*6 + 4*8 = 44 $$

Here the $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial x}$ should be evaluated at $(-1,1)$