f-x-y-xy-3-5xy-2-2x-1-find-f-x-f-y-f-xx-f-yy-f-xy-f-yx-

Question Number 7939 by tawakalitu last updated on 24/Sep/16

f (x, y) = {x y}^{3} + 5 {x y}^{2} + 2 x + 1

f i n d : f_{x}, f_{y}, f_{x x}, f_{y y}, f_{x y}, f_{y x}

Commented by Rasheed Soomro last updated on 25/Sep/16

{W h a t}^{'} s m e a n t b y f_{x y}, f_{x} e t c ?

Commented by tawakalitu last updated on 25/Sep/16

I s p a r t i a l d e r i v a t i v e

Commented by tawakalitu last updated on 25/Sep/16

o r f (x), f (x y), f (x x) \dots \dots

Answered by prakash jain last updated on 02/Oct/16

f (x, y) = {x y}^{3} + 5 {x y}^{2} + 2 x + 1

f_{x} = y^{3} + 5 y^{2} + 2

f_{y} = 3 {x y}^{2} + 10 x y

f_{x x} = 0

f_{y y} = 6 x y + 10 x

\frac{\partial}{\partial y} (\frac{\partial f}{\partial x}) = 3 y^{2} + 10 x

\frac{\partial}{\partial x} (\frac{\partial f}{\partial y}) = 3 y^{2} + 10 y