Answer to Question #252576 in Calculus for jose

Question #252576

f(x,y)=arctan(2x/(x^2+y^2))


1
Expert's answer
2021-10-18T16:57:53-0400

This question is incomplete but we can find "f_x" here

Given: "f(x,y)=arctan(2x\/(x^2+y^2))"

"f_x=\\frac{\\partial }{\\partial x}[arctan(2x\/(x^2+y^2))]\n\\\\=\\frac{1}{1+(2x\/(x^2+y^2))^2}. \\frac{\\partial }{\\partial x}[(2x\/(x^2+y^2))]\n\\\\=\\frac{(x^2+y^2)^2}{(x^2+y^2)^2+4x^2}.\\frac{(x^2+y^2).\\frac{\\partial }{\\partial x}(2x)-2x.\\frac{\\partial }{\\partial x}(x^2+y^2)}{(x^2+y^2)^2}\n\\\\=\\frac{2x^2+2y^2-4x^2}{(x^2+y^2)^2+4x^2}\n\\\\=\\frac{2y^2-2x^2}{(x^2+y^2)^2+4x^2}"


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