Consider the following equation.

$f(x,y)=\frac{y^3}{x},P(1,2),u=\frac{1}{3}(2i\sqrt[\phantom{2}]{5}j)$

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

gradf$(x,y)=$

$$

$($b$)$ Evaluate the gradient at the point $P.$

gradf$(1,2)=$

$$

$($c$)$ Find the rate of change of $f$ at $P$ in the direction of the vector $u.$

$D_{u}f(1,2)=$

$$