Question

Use the gradient to find the directional derivative of the function at P in the direction of Q.

f(x,y) = sin2xcosy, P(pi,0),Q(pi/2,pi)

Answer 1

For vector PQ I got -pi/2i-pi

Answer 2

how did you get that?

Answer 3

I took pi/2-pi , and pi-0 to get -pi/2i-pij

Answer 4

yeah ...okay that right!!! i understand!!

Answer 5

then would the unit vector where u=v/||v|| be -pi/2i-pij/[squarert(pi^2/4+pi^2)]?

Answer 6

yeah ... that would be correct!!

Answer 7

okay, i think i get it

d(PQ)/dr = gradient of f(x,y) .dot. unit vector

Answer 8

yeah thats the formula.

Answer 9

you have the unit vector above ... the gradient is

i 2 cos(2x).cos(x) - j sin(2x).sin(x)

Answer 10

yeah well i got thetaf(x,y)=2cos2xcosyi-sin2xsinyj

Answer 11

i haven't calculated, must be something like

-pi*cos(2x)(cosy)/|v|+pi*sin(2x) (sinx)/|v|

since it is a dot product, it should be scalar