Limit Notation	$\lim_{\Delta x→0} \frac{f(x+\Delta x)-f(x)} {\Delta x}$	$\lim_{h→0} \frac{f(x+h)-f(x)} {h}$
f’(x)	f prime of x		Names the function and the independent variable
y’	y prime		Nice and brief but does not name the independent variable and can get confusing if there is more than 1 function.
$\frac {dy}{dx}$	Derivative of function y with respect to a variable x	just like y prime but it shows the variable as x	Names both variables and uses d for derivative.
$\frac {df} {dx}$	"d dx of f at x" or "the
derivative of f with respect to x”		Emphasizes the function's name..
$\frac {d}{dx}[f(x)]$	Derivative of function f with respect to a variable x	just like $\frac {dy}{dx}$ but instead of y, it is f of x	Emphasis that differentiation is an operation performed on f.