This may seem like an overly trivial question, but I've just recently become confused about Langrange's 'prime' notation for derivatives (for example $f'(x)$).
I know for sure that $f'(x) = \frac{\delta f(x)}{\delta x}$.
But suppose we replace x with an expression, like 2x+1. Do we write $f'(x^2+1) = \frac{\delta f(x^2+1)}{\delta x}$ or $f'(x^2+1) = \frac{\delta f(x^2+1)}{\delta (x^2+1)}$?
Does putting the prime around the function instead of between its letter and parentheses make a difference? For example what does $(f(x^2+1))'$ mean?