Question

Please help me solve the following problem. Find the directional derivative of f at P in the direction of the vector a.
f(x,y)=(y^2)ln(x)
P(1,4)
a=<-3,3>

Answer 1

This is what I have done:
\[D _{a}f(x,y)=fx(x,y)(-3)+fy(x,y)(3)\]
\[=\frac{ y ^{2} }{ x }(-3)+2yln(x)(3)\]

Answer 2

My final answer @ P:
\[D _{a}f(1,4)=-48\]

The answer in the book:
\[-8\sqrt{2}\]

Answer 3

Ok I think I figured it out. I need to convert the vector (a) into a unit-vector.