Question

Letf(x,y)=xcosy. Calculate ∇f(x,y).

Answer 1

what does inverse triangle means?

Answer 2

with respect to x or y? dx or dy?

Answer 3

the symbol ∇ is called nabla.
∇f is read grad f or gradient f or del f, the last because nabla is an upside down delta.

that ∇f is a vector quantity. Strictly speaking, the correct way to write the gradient is ∇f(x,y) since the gradient is a vector quantity, and many texts do write it correctly. But this text does not even use bold font for the ∇, so we’ll follow the convention used here and omit the arrow above the ∇, and make the extra effort to remember ∇f is a vector quantity.

Answer 4

the gradient is just the vector .... looks like joyus beat me to it :)

Answer 5

haha! I know what it is just dont know how to find it

Answer 6

<df/dx, df/dy> use partials

Answer 7

f(x,y)=xcosy

df/dx = x(constant) = constant ... cos(y)

df/dy = constant(cos(y)) = constant(-sin(y)) ... -x sin(y)

Answer 8

grad f = cos(y) i - x sin(y) j or simply:
= <cos(y), -x sin(y)>

Answer 9

so i just find the partial with respect to x and respect to y and thats the answer right??

Answer 10

yep; the gradient is the "equation for the normal" at any given point. if that makes sense