Partial derivative question #2

Question

Problem:

$$ \text{Find}\: \frac{\partial{u}}{\partial{x}}\:\text{of}\:\:\:\:\: u=x^u+u^y $$
Would $\frac{\partial{u}}{\partial{x}}$ look like: $$ \frac{\partial{u}}{\partial{x}}=ux^{u-1}\frac{\partial{u}}{\partial{x}}+yu^{y-1}\frac{\partial{u}}{\partial{x}}?$$
Or possibly $$ \frac{\partial{u}}{\partial{x}}=x^u\log\left|x\right|\cdot\frac{\partial{u}}{\partial{x}}+y{u}^{y-1}\frac{\partial{u}}{\partial{x}}?$$
Where am I going wrong? All of the terms can't possibly have a $\frac{\partial{u}}{\partial{x}}$ attached to them or I couldn't separate and solve for it...