$$ x\cos y + y\cos u + u\cos x = 1 $$
I'm trying to calculate u$'_x$ and $u'_y$ in the point $(0,1)$ while $0 \leq u \leq \pi$.
I've managed to find:
$$u'_x = - \frac{\cos y-u\sin x}{\cos x-y\sin u}\\ u'_y = - \frac{\cos u-x\sin y}{\cos x-y\sin u}$$
What holds me back currently I can't find $u$.
I get to this equation when I place $(0,1)$ ----> $ \cos u + u = 1$
Thanks in advance, hope this question isn't too dumb.