Below is a function $f$. We are interested in how changes in the values of the input variables $x,y$ or parameters $a,b,c$ affect $f$. To that aim, we write as a function of both its input variables and its parameters, using the notation $f(x, y; a, b, c)$. The “gradient of towards $v$”, denoted as $\nabla v$ $f$, is the vector of all partial derivatives of $f$ to the variables/parameters listed in $v$.
$f(x, y; a, b, c)$ = $a$ $exp(2x)$ + $by^2$ + $cxy$
what is the answer to following:
- $\nabla x,y$ $f(x, y; a, b, c)$
- $\nabla a,b,c$ $f(x, y; a, b, c)$
- If $\delta$, $\epsilon$ are very small real numbers, what is $f(1,2; 3,4 + $$\delta$$, 5 + $$\epsilon$) $−$ $f(1,2; 3,4,5)$ approximately? Explain how you obtained the answer.