Question $10$

A function of two variables is given by $f(x,y)=2x+3x^{2}y-y^2.$

$($a$)$ Find expressions for the first.$-$order and second$-$order partial derivatives of $f.$

$($b$)$ Evaluate $fx(1,2)$ and $fy(1,2),$ and use the small increments formula to estimate the change in $f$ as $x$ increases by $0\mathrm{.}2$ and $y$ decreases by $0\mathrm{.}1$ at the point $(1,2).$