Find the directional derivative of:
z=11-.2x^(2)-(y^(2)/5) at (2,-6,3) in the direction
from A(2,-6,3) to B(4,-3,6).
We have the function f(x,y)=11-.2x^2-(y^2)/5, so
we must find AB. AB=(4-2)i+(-3+6)j=2i+3j
and we can find the unit vector u= v/(IIvII).
So u=2/(13^(1/2))i+3/(13^(1/2)j=(.5547i+.8321j)
grad f(x,y)=fx(x,y)i+fy(x,y)j=.4x^(.5)i+(2y)/5j
Then the direction of derivative at (2,-6)
Duf(2,-6)=grad f(2,-6)*u
=(.8i+2.4j)(.5547i+.8321j)
=(.44376+1.99704)
=2.4408
