Maximizing q in f(q)=q(Q-q) Derivation | Simplified Steps

[needhlp]

I am having trouble with this derivation: f(q)=q(Q-q). We want to find the values that maximize the vaule of q so the book sets the derivative equal to 0 and gets Q-2q=0

When I try to do the derivative of f(q)=q(Q-q), I used the product rule

1(Q-q) + q(Q-1)=0
Q-q+Qq-q=0
Q+Qq-2q=0

I have an extra (Qq) I don't know how to get rid of.

 

[Mark44]

I am having trouble with this derivation: f(q)=q(Q-q). We want to find the values that maximize the vaule of q so the book sets the derivative equal to 0 and gets Q-2q=0

When I try to do the derivative of f(q)=q(Q-q), I used the product rule

1(Q-q) + q(Q-1)=0

There's a mistake above. d/dq(Q - q) = -1, not Q - 1. Q is a constant in this function.

Q-q+Qq-q=0
Q+Qq-2q=0

I have an extra (Qq) I don't know how to get rid of.

 

[needhlp]

ah, too many q's running around. Thank you