Calculus is a unique branch of mathematics, and includes many symbols and equations that are also unique. Some are intuitive and make sense at a glance, but others can be very confusing if they are new to you. Here is a quick overview of some of the calculus symbols you will come across.
This is the format for writing a limit in calculus. When read aloud, it says “The limit of the function f of x, as x tends to 0.”
This is a common symbol indicating the derivative of the function f(x). It reads simply as “The derivative of f of x."
This is another symbol for a derivative. You can read it as “The derivative of y with respect to x.” Y is equivalent to f(x), as y is a function of x itself.
Both of these symbols represent the second derivative of the function, which means you take the derivative of the first derivative of the function. You would read it simply as “The second derivative of f of x.”
These symbols represent the nth derivative of f(x). Much like the second derivative, you would perform differentiation on the formula for n successive times. It reads as “The nth derivative of f of x.” If n were 4, it would be “The fourth derivative of x,” for example.
This is the symbol for differentiation with respect to time. You can read it as “the derivative of y with respect to time.”
This is called dot notation; more dots indicate higher orders of differentiation. For example: