1) f(x)=(2x-1)/(3x+2). If u=2x-1 and v=3x+2, du/dx=2 and dv/dx=3.
The derivative is (vdu/dx-udv/dx)/v^2=(2(3x+2)-3(2x-1))/(3x+2)^2=
(6x+4-6x+3)/(3x+2)^2=7/(3x+2)^2
2) f(x)=1/√x=x^(-1/2); f'(x)=-(1/2)x^(-3/2)=-1/√x^3
3) f(x)=√(x^2-1) needs the chain rule:
(1/2)(x^2-1)^(-1/2) * 2x=x/√(x^2-1)
4) f'(x)=2x+6