if-f-x-xlog-x-r-r-and-r-2-x-2-y-2-prove-that-f-xx-f-yy-1-x-r-

Tinku Tara June 3, 2023 Differentiation 0 Comments

Question Number 7938 by tawakalitu last updated on 24/Sep/16

if f(x) = xlog(x + r) − r and r^2 = x^2 + y^2 prove that: f_(xx) + f_(yy) = (1/(x + r))

$${if}\:\:{f}\left({x}\right)\:=\:{xlog}\left({x}\:+\:{r}\right)\:−\:{r}\:\:{and}\:\:{r}^{\mathrm{2}} \:=\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \\ $$$${prove}\:{that}:\:\:{f}_{{xx}} \:+\:{f}_{{yy}} \:\:=\:\:\frac{\mathrm{1}}{{x}\:+\:{r}} \\ $$

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if-f-x-xlog-x-r-r-and-r-2-x-2-y-2-prove-that-f-xx-f-yy-1-x-r-

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