Answer to Question #107192 in Calculus for Nikesh gautam pandit ji

Question #107192
Compute fxy and fyx for the function f(x,y) = e^(x+y) +9x^2 +2xy at (1,2).
1
Expert's answer
2020-04-02T13:14:01-0400

"f(x,y)=\\exp^{x+y}+9x^2+2xy."

Find "f_{xy}" and "f_{yx}" at (1,2).

Find first "f_x" and "f_y"

"f_x=\\frac{\\partial}{\\partial x}(\\exp^{x+y}+9x^2+2xy)=\\exp^{x+y}+18x+2y,"

"f_y=\\frac{\\partial}{\\partial y}(\\exp^{x+y}+9x^2+2xy)=\\exp^{x+y}+2x."

To find "f_{xy}" and "f_{yx}" take the partial derivative of "f_{x}" with respect to "y" and "f_{y}" with respect to "x" respectively.

"f_{xy}=\\frac{\\partial}{\\partial y}(\\exp^{x+y}+18x+2y)=\\exp^{x+y}+2,"

"f_{yx}=\\frac{\\partial}{\\partial x}(\\exp^{x+y}+2x)=\\exp^{x+y}+2."

So,

"f_{xy}(1,2)=f_{yx}(1,2)=\\exp^{1+2}+2=\\exp^{3}+2".


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