show that the following function is C1 (and is therefore differentiable) in its domain:

f(x, y) = x/y + y/x show that the following function is C1 (and is therefore differentiable) in its domain:

f(x, y) = x/y + y/x @Mathematics

Question

show that the following function is C1 (and is therefore differentiable) in its domain:

f(x, y) = x/y + y/x show that the following function is C1 (and is therefore differentiable) in its domain:

f(x, y) = x/y + y/x @Mathematics

amistre64 · Answer

this one i assume

anonymous · Answer

C1 means that the derivative is continuous

amistre64 · Answer

is that  y(x) or just another independant variable?

anonymous · Answer

another independent variable. just say it's z

amistre64 · Answer

f(x, y) = x/y + y/x

$$\frac{\delta f}{\delta x}=\frac{1}{y}-\frac{y}{x^2}$$
$$\frac{\delta f}{\delta y}=-\frac{x}{y^2}+\frac{1}{x}$$
not sure if thats useful ....

amistre64 · Answer

the domain excludes y,x = 0 im sure

amistre64 · Answer

found someting similar at: http://www.cds.caltech.edu/~marsden/wiki/uploads/math1c-08/assignments/homework_sol3.pdf

amistre64 · Answer

the function simplifies to: f(x, y) = (x^2+y^2)/xy ; domain such that x or y not 0 $$F_x=\frac{x^2y-y^3}{x^2y^2}$$ $$F_y=\frac{xy^2-x^3}{x^2y^2}$$ exclude x=0 and y=0, these might not be continuous http://www.wolframalpha.com/input/?i=%28x%5E2y-y%5E3%29%2F%28x%5E2y%5E2%29