i have come cross this question:
A function f: R2 -> R is defined by f(x,y) = g(x-2y), where g: R -> R. If g'(1) = 3, calculate fx(3,1) and fy(3,1). Show that fy(x,y) = -2 * fx(x,y) in general.
Let q(x) = x-2y. So, I think that f(x,y) = g(x-2y) as f(x,y) = g(q(x)), so f'(x,y) = g'(q(x)) * q'(x).
so, fx(x,y) = g'(q(x)) * (1-2y) and fy(x,y) = g'(q(x)) * (x-2) then fx(3,1) = -3 and fy(x,y) = 3.
But looking at the prove of fy(x,y) = -2 * fx(x,y) I think my answer for the fy(3,1) is wrong. Could someone please help me?
ps. I was just wondering is there any function that is biger then ln?
Thanks.
Helen
A function f: R2 -> R is defined by f(x,y) = g(x-2y), where g: R -> R. If g'(1) = 3, calculate fx(3,1) and fy(3,1). Show that fy(x,y) = -2 * fx(x,y) in general.
Let q(x) = x-2y. So, I think that f(x,y) = g(x-2y) as f(x,y) = g(q(x)), so f'(x,y) = g'(q(x)) * q'(x).
so, fx(x,y) = g'(q(x)) * (1-2y) and fy(x,y) = g'(q(x)) * (x-2) then fx(3,1) = -3 and fy(x,y) = 3.
But looking at the prove of fy(x,y) = -2 * fx(x,y) I think my answer for the fy(3,1) is wrong. Could someone please help me?
ps. I was just wondering is there any function that is biger then ln?
Thanks.
Helen