$(1$ point$)$ Suppose $f(x,y)=\frac{x}{y},P=(4,-1)$ and $v=2i-1j.$

A$.$ Find the gradient of $f.$

gradf$=ij$

Note: Your answers should be expressions of $x$ and $y$; e$.$g$."3x-4y"$

B$.$ Find the gradient of $f$ at the point $P.$

$(gradf)(P)=,i$

Note: Your answers should be numbers

C$.$ Find the directional derivative of $f$ at $P$ in the direction of $v.$

$D_{u}f$

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Note: Your answer should be a number

D$.$ Find the maximum rate of change of $f$ at $P.$

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Note: Your answer should be a number

$E.$ Find the $($unit$)$ direction vector in which the maximum rate of change occurs at $P.$

$u=$

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Note: Your answers should be numbers