Thread: vector calculus - vector feilds

find the gradient vector feild ∇f of f and sketch it

f(x,y) = sqrt(x^2 +y^2)

Originally Posted by oohaysomeone

find the gradient vector feild ∇f of f and sketch it

f(x,y) = sqrt(x^2 +y^2)

Do you know the definition of ∇f? Where is your impediment in applying it?

to find the gradient, i think i have to follow this formula:

∇f (x,y) = (fx, fy)

i think the first order partial derivitives will then be:

dF/dx = (1/2) * 2x * (x^2 + y^2)^(-1/2) = x * (x^2 + y^2)^(-1/2)

dF/dy = (1/2) * 2y * (x^2 + y^2)^(-1/2) = y * (x^2 + y^2)^(-1/2)

is this right? what step would i take next and how would i sketch this?

Originally Posted by oohaysomeone

to find the gradient, i think i have to follow this formula:

∇f (x,y) = (fx, fy)

i think the first order partial derivitives will then be:

dF/dx = (1/2) * 2x * (x^2 + y^2)^(-1/2) = x * (x^2 + y^2)^(-1/2)

dF/dy = (1/2) * 2y * (x^2 + y^2)^(-1/2) = y * (x^2 + y^2)^(-1/2)

is this right? what step would i take next and how would i sketch this?

You've more or less done it. To draw the vector field, you're probably expected to substitute values of x and y and then draw a small directed line segment at that point. I'm sure your textbook or notes will have examples.