Question

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

Answer 1

$f_x'=e^{x+y}\sin x+e^{x+y}\cos x+18x+2y$ , $f_{xy}''=e^{x+y}\sin x+e^{x+y}\cos x+2$

$f_y'=e^{x+y}\sin x+2x$ , $f_{yx}''=$$e^{x+y}\sin x+e^{x+y}\cos x+2$ then

$f_{xy}''=f_{yx}''=e^{x+y}(\sin x+\cos x)+2\approx29.8$ at $(x,y)=(1,2)$