1. The problem is to find the derivative of the expression $(xy)' + (x' + y')$. 2. Recall the product rule for derivatives: $\frac{d}{dx}(uv) = u'v + uv'$, where $u$ and $v$ are functions of $x$. 3. Applying the product rule to $(xy)'$, we get: $$ (xy)' = x'y + xy' $$ 4. The expression becomes: $$ (xy)' + (x' + y') = x'y + xy' + x' + y' $$ 5. Group like terms: $$ (x'y + x') + (xy' + y') = x'(y + 1) + y'(x + 1) $$ 6. This is the simplified form of the derivative expression. Therefore, the answer is: $$ (xy)' + (x' + y') = x'(y + 1) + y'(x + 1) $$