If fxy find the domain of f xY Verify Clairauts Theorem by

If f(x,y) = , find the domain of f (x,Y). Verify Clairaut\'s Theorem by showing that f xy = f yx.

Solution

for ln to define
4x² - y>0

4x² > y

again x+y > = 0

so domain is

x > = -y and 4x² > y

fx = 8x/(4x² -y) -1 +0.5/(x+y)

fy = -1/(4x² -y) +0.5/(x+y)

fyx = -8x/(4x² -y)² - 0.25/(x+y)^3/2

fxy =  -8x/(4x² -y)² - 0.25/(x+y)^3/2

hence clairauts therom verified