Directional Derivatives

[engineertobe]

Part 1:
A happy heat-loving bug is wandering on a hot plate. The temperature at any point on the plate is given by
T(x

y)=260e−(x2

4)−(y2

3)
If the bug is at the point P=(−1

1) and moving towards the point Q=(3

−3), what is the rate of change in the temperature in the direction of its motion?

I got (260e^(-.25-(1/3)))((.5(4/sqrt(32)))+(-2/3)(-4/sqrt(32))). It is correct.

Part 2:
In what direction should the bug move from P for the temperature to increase the fastest? (Give your answer as a unit vector.)

I got <130e^(-.25-(1/3))/120.9076, 260e^(-.25-(1/3))(2/3)/120.9076> the first coordinent is correct, the second is wrong.

Part three:
What is the magnitude of the rate of change of temperature in that direction?

I got 120.9076 it was right. I know I am on the right track but what did I do wrong for the second part of the second part?