Differentiate 80*[sqrt (500^2+x^2)] + 50*(800-x)

Differentiate 80*[sqrt (500^2+x^2)] + 50*(800-x).

I've started by

80*[sqrt (500^2+x^2)] + 50*(800-x)

=80* (250000 + x^2)^(1/2) + 50*(800-x)

Now that I've set the question up to differentiate, I don't know what the next step would be if I was to use the product rule

Would it look something like this

Using the Chain Rule for:80* (250000 + x^2)^(1/2)

40(250000+x^2)^(-1/2) * 2x

Again I am not sure of my workings if its correct on this one

Please. Can someone walk me through this problem step by step so I understand how you can derive this function??

Thanks