Directional Derivative of a Multivariable Function

[freecw]

Homework Statement

Find the directional derivative of f at P in the direction of a.
f(x,y)=y²lnx; P(1,4); a= -3i + 3j

Homework Equations

The Attempt at a Solution

I first normalized the vector and got a_n = -3/(18)^1/2 + 3/(18)^1/2
Then i took the partial derivative and multiplied it by the vector
y²/X(-3/18^1/2) + 2(y)lnx(3/18^1/2
Ln(1) = 0 so the whole right side is gone, and after i plug in 1 and 4 on the right side i get -16/2^1/2. The answer should be -8/2^1/2. I've done 5 problems like this now and each time I'm off by a negative or a factor or something like that. What am i doing wrong?

 

[Dick]

I get -16/sqrt(2) as well. Are you sure the answer wasn't -8*sqrt(2)? That would be the same thing you have.

 

[freecw]

Thanks, i just went back and checked the back of the book, the answer is supposed to be -8*sqrt(2) not -8/sqrt(2). Also i didn't notice that -16/sqrt(2) is the same thing as -8*sqrt(2). Thanks for the help.