If you want to represent f*f*f*f*f, you might enter f^5. In standard notation in calculus, derivatives are denoted by primes, such as f', f''.

At a certain order of derivative, entering and counting the number of primes becomes cumbersome. For example, what is f''''''''''?

Bracketed number notation is used to describe a derivative, so the above is written as f^(10), where the brackets are redundant. These redundant brackets are the key between detecting this notation as opposed to just f times itself 10 times, which is f^10.

For example:

f^5 -> f*f*f*f*f

f^(5) -> diff(f(x),x,x,x,x,x)

The ability to turn off this notation is necessary in the following example cases.

f^(#)

f^(n)

(expr)^(#)

(expr)^(n)

Where in the above '#' is a positive number, and 'n' is any single variable.

Note: The following cases do not apply for the reasons indicated.

f^(a+b) -> Brackets are redundant, are needed, and always a power.

(f+x)^(a+b) -> Brackets are redundant, are needed, and always a power.

f^(n)(x) -> Functions are not included, and have different rules.

sin^(n)(x) -> Same as above, includes known functions.

For the cases in which the rule does apply:

The always setting interprets the redundant brackets always as derivatives.

The never setting interprets as a power.