Derivative of y=(p-1)x+p+1p=dy/dx

1. Differentiate $p + \left(p + x \left(p - 1\right)\right)$ term by term:

   1. Differentiate $p + x \left(p - 1\right)$ term by term:

      1. The derivative of a constant times a function is the constant times the derivative of the function.

         1. Apply the power rule: $x$ goes to $1$

         So, the result is: $p - 1$

      2. The derivative of the constant $p$ is zero.

      The result is: $p - 1$

   2. The derivative of the constant $p$ is zero.

   The result is: $p - 1$

2. Now simplify:

   $$p - 1$$

The answer is:

$$p - 1$$