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The system of equations:

$x-u^2-v^2+9=0$

$y-u^2+v^2-10=0$

defines $(u,v)$ as a function of $(x,y)$ in every point $u\cdot v\ne 0$

I wish to find $u_{xx}$

I managed to find $u_x$:

if $F=(x-u^2-v^2+9,y-u^2+v^2-10)$ than $u_x=\frac{\partial u}{\partial x}=\frac{1}{4u}$

but i have no idea how to find the second derivative.

any ideas? (the answer is $-\frac{1}{16u^3}$)

segevp
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1 Answers1

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Well $$ u_{xx}=\frac{\partial}{\partial x}u_x=\frac{\partial}{\partial x}\frac{1}{4u}=-\frac{1}{4u^2}u_x=-\frac{1}{16u^3} $$

Vincenzo Tibullo
  • 10,955