Solving a differential equation through substitution In a book an example is given:

Solve  $\frac{dy}{dx} = (x+y-4)^2$ by first making an appropriate substitution.

In the solution a step is given which I don't understand:

We let $u = x+y-4$ and thus $\frac{dy}{dx} = u^2$. We need to calculate $\frac{du}{dx}$. For this example, taking the derivative with respect to x gives $$\frac{du}{dx} = 1+\frac{dy}{dx}.$$

The last step I cannot follow, where does the summand $\frac{dy}{dx}$ come from?
I tried $\frac{dy}{dx} = u^2 = \frac{dy}{du}\cdot 1 = \frac{dy}{du}\cdot \frac{du}{dx}$ yielding the solution $y = \frac{1}{3}(x+y-4)+C$ which is definately wrong.

Given that $u=x+y-4$, clearly, differentiating with respect to $x$ gives $$\frac{du}{dx}=1+\frac{dy}{dx}.$$
