Question

If → u = 3/5 →i - 4/5→j, find D→u f (2, pi/3)
DESPERATE!!

Answer 1

problem 1 part b

Answer 2

It want directional derivative

Answer 3

\[ f(x, y) = x cos y \]
let's find Gradient
\[\nabla f=<cos (y),-xsin (y)>\]
In the direction of \[\frac{3}{5}i-\frac{4}{5}j\]


This is the unit vector since magnitude is 1

Now take dot product
\[<3/5,-4/5>.<cos (y),-xsin (y)>\]
\[\frac{4}{5} x \sin (y)+\frac{3 \cos (y)}{5}\]

Plug in value (x,y) --> (2,pi/3)

\[\frac{3}{10}+\frac{4 \sqrt{3}}{5}\]

Answer 4

that's all??

Answer 5

yes

Answer 6

oh wow! Thank you!!!! have been stuck on this problem for 2 days I was thrown off the the D vector u

Answer 7

u r a life saver!

Answer 8

wow, you've asked this question like how many times? glad I could help