I have this $f(x,y)$. $x$, $y$ and the output of of $f$ will always be positive numbers. $x$ and $y$ are independents. I am trying to find $df$, which is just ...
$$df=\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy$$
But I only have the inputs $x$ and $y$ and the output of $f$, the equations are hidden from me. So, I can only use the regular slope formula $(rise/run)$ to find the derivatives between x-axis and y-axis, such as ...
$$df=[f(3,5)-f(2,5)]+[f(3,5)-f(3,4)]$$ $$=(2403-12)+(2403-376)$$ As you can see, the output of $f$ is somewhat "random", it can be big or small, but the same $x$ and $y$ will yield the same output such as $f(1,3)$ will always produce $520$. So the question now is; am I correct on trying to find the derivative values by using the regular slope formula?
I am not trying to solve the equation or predict the future value, but I just wanted to be able to tell what is happening with the output as in "has $f$ increased or decreased?" and by finding the higher derivative I can answer the question "if $f$ has increased, is it stopping or continuing?".