$(3)$ Consider the function $f(x,y)=x-y^2$ and the point $P=(2,2).$

$($a$)$ Find the gradient of $f$ at $P.$

$($b$)$ Find the directional derivative of $f$ in the direction of vec$(v)=3$vec$(i)-$vec$(j)$ at $P.$

$($c$)$ Draw the level set of $f$ that contains $P.$

$($d$)$ Draw the gradient of $f$ at $P$; put the tail of the gradient on $P.$