Directional derivative?

[cabellos]

Im doing the following question:

calculate the directional derivative of the function f(x,y,z) = z/(2x + y) at the point (0,1,1) in the direction d = 2i - 2j - k

could someone please check my answer is correct as i calculated -3i -6k

Also how do i find the unit vector in the direction of the greatest rate of change of the function f(x,y,z)

thanks

 

[Dick]

Think again. The directional derivative of a scalar function is not a vector. Hint: look at the concept of gradient.

 

[cabellos]

the gradient i found was -2z/(2x+y)^2 i + -z/(2x+y)^2 j + 2x+y/(2x+y)^2 k

i thought the directional derivative was then s.grad

what should the answer be?

 

[Dick]

It IS s.grad. But s.grad is a scalar.

 

[cabellos]

ok sorry. i think iv got the answer now. -1 ?

 

[Dick]

What is your vector for grad? You'd better check arithmetic...

 

[Dick]

I've got to go now. But as for your second question, if derivative is s.grad, what direction should s point to maximize the derivative?

 

[cabellos]

how about -3?

 

[Dick]

-3? I like it.