Derivative of long expression renders Piecewise[…<<…>>…] in Jupyter notebook

Question

My mathematical problem is to solve the optimization problem: $$ Max_{u} \quad \mathbb{E}[\gamma S-S^2]$$ where $$S= A_0 u X+a-\max(\alpha u X+b,0)$$ with $\gamma,A_0,a,\alpha,b$ some constants and $X\sim N(\mu,\sigma)$.

As a starting point, I was trying to compute the tedious expectation via

Expectation[gamma*(a0*u*x+a-Max[alp*u*x+b,0])-((a0*u*x+a-Max[alp*u*x+b,0]))^2, x \[Distributed] NormalDistribution[mu, sig]]

and here is the output:

using the Wolfram Engine (via Jupyter Interface). After that, I was trying to take the partial derivative with respect to $u$ using

D[%,u]

and it renders a very strange output:

My feeling is that the expression is so long that it is unable to display it so the problem is not from the mathematical difficulty but more from the display. I searched on stackexchange but couldn't find a similar issue.

Do you know what the exact issue is and I can get the proper derivative ?

Thanks a lot !

Edit: The problem is now solved thanks to the solution below. Since some people comment that they can't recover my output, here is the full Jupyter output:

Answer 1

Clear["Global`*"]

To get the simplest form you need to tell Mathematica any constraints on the variables. For example,

$Assumptions = {mu ∈ Reals, sig > 0, alp > 0, u > 0, b > 0};

$Assumptions will automatically be used by any function that uses the option Assumptions (e.g., Expectation, FullSimplify)

expr = Expectation[
   gamma*(a0*u*x + a - 
       Max[alp*u*x + b, 0]) - ((a0*u*x + a - Max[alp*u*x + b, 0]))^2, 
   x \[Distributed] NormalDistribution[mu, sig]] // FullSimplify

(* 1/2 (-2 a^2 - 
   b (b + gamma) - (-2 a0 (b + gamma) + 
      alp (2 b + gamma)) mu u - (2 a0^2 - 2 a0 alp + alp^2) (mu^2 + 
      sig^2) u^2 + 2 a (b + gamma + (-2 a0 + alp) mu u) - 
   alp E^(-((b + alp mu u)^2/(2 alp^2 sig^2 u^2))) Sqrt[2/π]
     sig u (-2 a + b + 
      gamma + (-2 a0 + alp) mu u) + (-b (-2 a + b + 
         gamma) + (2 a alp + 2 a0 b - alp (2 b + gamma)) mu u - 
      alp (-2 a0 + alp) (mu^2 + sig^2) u^2) Erf[(b + alp mu u)/(
     Sqrt[2] alp sig u)]) *)

Taking the derivative

D[expr, u] // FullSimplify

(* a (-2 a0 + alp) mu + a0 (b + gamma) mu - 
 1/2 alp (2 b + gamma) mu - (2 a0^2 - 2 a0 alp + alp^2) (mu^2 + 
    sig^2) u + (
 E^(-((b + alp mu u)^2/(2 alp^2 sig^2 u^2)))
   sig (-2 a0 b - alp (-2 a + gamma + 2 (-2 a0 + alp) mu u)))/Sqrt[
 2 π] + 
 1/2 ((2 a alp + 2 a0 b - alp (2 b + gamma)) mu - 
    2 alp (-2 a0 + alp) (mu^2 + sig^2) u) Erf[(b + alp mu u)/(
   Sqrt[2] alp sig u)] *)