find the derivative of y
y=
2 (22x+31)^(3/2)+ arctan((22x+21)^(1/2))+ln(11x+16)-22x-30
d/dx u^n = nu^(n-1) u'
d/dx arctan(u) = 1/(1+u^2) u'
d/dx ln(u) = 1/u u'
So, we have
y' = 2(3/2) √(22x+31) * (22)
+ 1/(1+(22x+21)) * (1/2) * 1/√(22x+21) * 22
+ 1/(11x+16) * 11
- 22
= 66/√(22x+31) + 11/((22x+22)√(22x+21)) + 11/(11x+16) - 22