Question 1024224
I will assume that your function is {{{y = (x+1)sqrt(x+8)}}}.  If 8 is outside the radical the procedure is entirely similar.

{{{dy/dx = (d(x+1)/dx)(sqrt(x+8)) + (x+1)(d(sqrt(x+8))/dx)}}}

={{{1*sqrt(x+8) +(x+1)*(1/(2sqrt(x+8)))}}}

={{{sqrt(x+8) + (x+1)/(2sqrt(x+8))}}}

={{{(3x+17)/sqrt(x+8)}}}