Exercise $3$

Find the directional derivative $D_{u}f(x,y),$ for

$(1)f(x,y)=x^3-3xy+4y^2$ and $u=(\frac{1}{4},\frac{\sqrt[\phantom{2}]{15}}{4})$

$(2)f(x,y)=xln(1+y^2)$ and $u=(\frac{1}{3},\frac{\sqrt[\phantom{2}]{8}}{3})$