Alternate Notation : Next we have to discuss some alternate notation for the derivative. The typical derivative notation is the "prime" notation. Though, there is another notation which is used on occasion hence let's cover that.

Given a function y = f ( x ) all of the given are equivalent & represent the derivative of f (x) w.r.t. x.

f ′ ( x ) = y′ = df/dx= dy/dx = d ( f ( x )) = d ( y )/dx

Since we also have to evaluate derivatives on occasion we also require a notation for evaluating derivatives while using the fractional notation.  Thus if we desire to evaluate the derivative at x=a all of the given are equivalent.

Note that we will drop the (x) part on the function to simplify the notation fairly.  In these cases the following are equivalent.

f ′ ( x ) = f ′