Well, I do understand what Df is and how you find it in simple equations, however, I am kinda confused in "complex" functions.
For example, the following functions: 1* f(x)=x^3+x^2-x-1 , Df=R (however, I don't understand why.)
2* f(x)=2x/(1+x^2), we have to find Df for 1+x^2, therefore Df=R, I do understand this one.
3* f(x)=2x^2-x^4 , Df=R (Don't know why)
4* f(x)=x^2/(x-2), Df=R (don't know why)
Could anyone explain why is the Df always R in this cases?