Let $f(x,y)$ be a differentiable function of two variables. Suppose at the point $(1,1)$ fincreases most rapidly in the direction of $A=i+2j.$ Also suppose that gradf$(3,-3)=6i-2j,$gradf$(-7,7)=3i-j,f(-7,7)=1,f(9,-9)=5.f_x(1,1)=2.$ In addition, suppose that the level curve of $f$ passing by the point $(9,-9)$ also passes by the point $(3,-3).$ and that the tangent line to the level curve of f at $(1,2)$ also passes by the point $(7,7).$ Finally let. $x=r^2-s^2,y=s^2-r^2,$ and $w=f(x,y)$

$($a$)$ Find $\frac{dw}{dr}$ and $\frac{dw}{ds}$ at the point $(r,s)=(2,1).$ Then estimate $w(2\mathrm{.}1,0\mathrm{.}9).$

$($b$)$ Find $D_{4}w(2\mathrm{.}1)$ in direction of $u=i+j$

$($c$)$ Find gradf$(1,1).$

$($d$)$ Estimate $(13\mathrm{.}1,-2\mathrm{.}9).$