Problem 1280 (difficulty: 4/10)

For \(\displaystyle |x|<1\), \(\displaystyle |y|<1\), \(\displaystyle |z|<1\) let \(\displaystyle u(x,y,z)\) be the real root of

\(\displaystyle (2+x)u^3+(1+y)u-(3+z)=0. \)

Find \(\displaystyle u'(0,0,0)\).

Give me another random problem!