Question

Compute fxy and fyx for the function f (x,y)=e^x+y sinx +9x^2+2y at (1,2)

Answer 1

$f (x,y)=e^x+y sinx +9x^2+2y$

$f_{xy}=(f_x)_y= \frac{\partial }{\partial y}(\frac{\partial f}{\partial x})$

$=\frac{\partial }{\partial y}(e^x+ycosx+18x)$

$=cosx$

Thus, $f_{xy}(1,2)=\cos(1)$

$f_{yx}=(f_y)_x= \frac{\partial }{\partial x}(\frac{\partial f}{\partial y})$

$=\frac{\partial }{\partial x}(sinx+2)$

$=cosx$

Thus, $f_{yx}(1,2)=cos(1)$