Math Help - Maximum Profit

The demand for a certain product is given by the model p=53/sqrt(x). the fixed costs are $608 and the cost per unit is $0.53. Find the production level x that yields the maximum profit if x is between [0,7530]

I know that P=R-C and thats about it

After thinking about this I tried to do it, can somebody please check my work

P=R-C
R=xp C=0.53x+608
R=53x/sqrt(x)

P=53x/sqrtx-0.53x-608
P=53sqrt(x)-0.53x-608
DP/dx=53/2sqrt(x)-0.53
0=53/sqrt(x)-0.53
x=2500


Please Help