1. The problem statement, all variables and given/known data I have two questions. First: What is the derivative of u(w)=k-e^(-aw) Second: For U(w)=sqrt(w), prove that U(pie(x)+(1-pie)y) > pie*U(x)+(1-pie)U(y) 2. Relevant equations 3. The attempt at a solution For the first one, I haven't seen this type of problem in so long that I just don't remember how to take a derivative in this form. Would it be: u'(w)= -(-aw)e^(-aw-1)*-a =(aw)e^(a^2w+a)? I wasn't sure if the chain rule was appropriate here. For the second question, I have: sqrt(pie(x)+(1-pie)y) > pie*sqrt(x)+(1-pie)sqrt(y) so... (pie(x)+(1-pie)y)^(1/2) > pie*(x)^1/2+(1-pie)(y)^1/2 From here I don't know where to go. I don't have much experience with proofs so can anyone give some guidance? Thanks for your help!