show that fxy =fyx for f(x,y)= x sqrt(y-x^2)
when i find do this they are not equal but from the definition they are supposed to be...can some one show me the work to compare it to mine so i can see where i messed up???
$\displaystyle f(x, y) = x \sqrt{y - x^2}$
$\displaystyle f_x = \sqrt{y - x^2} + x \cdot \frac{1}{2 \sqrt{y - x^2}} \cdot -2x$
$\displaystyle f_x = \sqrt{y - x^2} - \frac{x^2}{\sqrt{y - x^2}}$
$\displaystyle f_{xy} = \frac{1}{2\sqrt{y - x^2}} + \frac{x^2}{2(y - x^2)^{3/2}}$
You do $\displaystyle f_{yx}$.
-Dan