Hello all math geniuses out there here is a question that probably does require much thinking, but i can't seem to figure out.
The equation $x^3 +yz-xz^2=0$ implicitly defines a function $z=f(x,y)$ for which $f(-2,1)=2$. Calculate $f_x(-2,1)$
Here is how i think about it $$f_x= 3x^2-z^2$$ $$f_y= z$$ $$f_Z=y-2xz$$ should I just evaluate everything at $(-2,1)$ or what?
Honestly every answer below is satisfying and i dont know who to give best answer for so i am just gonna give it to the first one. The rest thank you for your time